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PRACTICAL   HINTS 


FOR 


DRAUGHTSMEN. 


BY 


CHARLES   WILLIAM   JVUcCORD,   A.M.,   Sc.D., 

'• 

Professor  of  Mechanical  Drawing  in  the  Sterens  Institute  of  Technology,  Hoboken,  N.  J. ; 

Author  of  a  '•  Treatise  on  Kinematics"  "Lessons  in  Mechanical  Drawing" 

"A  Practical  Treatise    on  the  Slide   Valve  and  Eccentric" 

and  Various  Monograptis  on  Mechanism. 


SECOND  EDITIOX. 


UKI7BBSITT 


NEW   YORK  : 

JOHN    WILEY    &    SONS, 

15  ASTOR  PLACE. 
1888. 


COPYRIGHT,  1888, 
BY  CHARLES  WILLIAM  MAcCORD. 


DRHMMOND  &  NEC,  FERRIS  BROS.. 

Electro!  apers,  Printers, 

1  to  7  Hague  Street,  336  Pearl  Street, 
New  York.  New  York. 


PREFACE. 


THE  leading  object  of  this  treatise  is  to  explain  various  modes  of  representation 
which  are  in  many  cases  better  than  the  precise  ones  of  projection :  for  mechanical 
drawings  often  convey  false  impressions  by  too  close  adherence  to  the  truth,  and 
become  obscure  by  being  too  exact. 

All  working  plans  are  made  for  the  purpose  of  showing  what  is  to  be  done, 
and  should  exhibit  the  maker's  knowledge,  not  of  the  refinements  of  theory,  but  of 
the  requirements  of  practice.  They  are  to  a  considerable  extent  beyond  the  jurisdic- 
tion of  the  rigid  laws  of  descriptive  geometry,  and  to  that  extent  they  lie  within 
the  domain  ruled  by  plain  common-sense.  This  fact  is  often  not  duly  impressed 
upon  the  mind  of  the  student ;  which  is  unfortunate,  because  no  one  thing  is  more 
fatal  to  practical  efficiency  than  thr  ^strict  formalism  which  subordinates  the  end  to 
the  means,  allows  no  exercise  of  discretion,  and  binds  the  draughtsman  to  the 
observance  at  all  times  of  inflexible  rules. 

It  is  hoped  that  the  reader  will  escape  such  thraldom  in  either  constructing 
drawings  to  scale  or  making  sketches ;  both  of  which  are  illustrated  by  a  number  of 
practical  examples  of  approved  methods. 

The  addition  of  the  chapter  on  drawing  instruments  is  justified  by  the  fact  that 
in  most  treatises  upon  drawing,  mere  descriptions  or  illustrations  are  given,  with 
nothing  to  guide  the  novice  in  distinguishing  the  good  from  the  bad :  and  also  by 
the  reception  of  numerous  letters  of  inquiry,  from  those  desirous  of  information  upon 
this  very  important  and  much-neglected  matter. 

C.  W.  MACCORD. 

HOBOKEX,  N.  J.,  August   22,  1887. 


CONTENTS. 


CHAPTER  I. 

FACE 

WORKING  DRAWINGS  DEFINED.     RULES  OF  PROJECTION    DEFIED.     CLEARNESS  AND  CERTAINTY 
THE  ESSENTIAL  REQUISITES.     ILLUSTRATIVE  EXAMPLES, i 

CHAPTER   II. 

ON  THE  REPRESENTATION  OF  BOLTS,  NUTS,  SCREWS,  AND  RIVETS, 37 

CHAPTER   III. 

FREE-HAND  SKETCHING.     SKETCHING  IN  PROPORTION.     ITS  UTILITY  IN  DESIGNING.    SKETCHING 
FROM  MEASUREMENT.    METHODS  OF  PRACTISING.    PRACTICAL  SUGGESTIONS  AND  EXAMPLES,  .    47 

CHAPTER   IV. 
DRAWING  INSTRUMENTS  AND  MATERIALS 63 

APPENDIX. 

PROPORTIONS  OF  BOLTS.  NUTS,  THREADS,  AND  BOLT-HEADS,   ACCORDING  TO  THE  SELLERS  AND 
THE  WHITWORTH  SYSTEMS 95 

INDEX,  .  •; 99 


OF 

UH1VBRSIT7 


PRACTICAL   HINTS    FOR    DRAUGHTSMEN. 


CHAPTER     I. 

WORKING     DRAWINGS      DEFINED.       RULES      OF      PROJECTION     DEFIED.        CLEARNESS      AND 
CERTAINTY    THE    ESSENTIAL    REQUISITES.      ILLUSTRATIVE    EXAMPLES. 

1.  Mechanical   Drawings    are   made    in    the    main    according    to    the   principles    of 
projection,  which    constitute   a   part    of    the   science    of    descriptive    geometry ;    but    even 
a   perfect   acquaintance   with    that   science   will    not   of    necessity   or    of    itself    make   its 
possessor   an    efficient    practical    draughtsman,  no    matter   how   skilful    he    may   also   be   in 
the   manipulation   of   the   instruments. 

The  object  of  working  drawings  is,  to  show  the  workman  what  to  make  and  how 
to  make  it,  which  they  should  do  in  a  distinct  and  unmistakable  manner.  And  it 
is  amply  proved  by  experience,  that  drawings  may  be  in  themselves  absolutely  correct, 
and  fail  nevertheless  to  accomplish  this  object.  The  meaning  may  be  there ;  but  if 
it  is  not  clearly  and  forcibly  expressed,  the  work  is  radically  bad,  though  never  so 
finely  executed. 

Other  things  being  equal,  he  is  the  most  valuable  man  in  the  drawing  office 
who  can  with  the  least  outlay  of  time  and  labor  produce  such  work-  as  will  enable 
the  construction  to  be  carried  forward  with  certainty  and  dispatch.  To  this  end  his 
drawings  must  be  easily  read  and  well  arranged ;  it  will  not  suffice,  as  many  suppose, 
that  they  b*  correct  as  studies  of  projection.  It  is  well  that  the  draughtsman  should 
be  master  of  the  principles  of  his  science,  but  in  the  practice  of  his  art  he  should 
not  be  their  slave ;  perspicuity  is  as  important  as  accuracy,  and  judicious  defiance 
of  rigid  rules  will  often  result  in  a  gain  in  this  respect  as  well  as  in  a  saving  of 
time. 

2.  It    is    mainly    to     such     irregularities     that     the     following     pages     are    devoted ; 
supposing    the    reader     to     be     already     familiar    with     the     laws    of    projection,    it    is 
proposed   to   show   how   and   when    those   laws   may   be   broken   with    impunity. 

This  cannot  be  done  wholly  by  laying  down  specific  instructions ;  it  would  be 
difficult  if  not  impracticable  so  to  classify  exceptions  as  to  deduce  from  them  rules 
that  would  cover  the  whole  ground,  or  be  of  universal  application.  New  devices  and 
new  combinations  are  continually  arising,  special  features  of  which  may  require  special 
treatment,  and  there  is  constant  occasion  for  the  exercise  of  judgment  and  ingenuity. 

The   general    plan   adopted    therefore    is,  to   illustrate    the    matter    by   a   number   of 


2  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 

examples  selected  from  practice,  explaining  in  each  case  the  particulars  in  which  it 
violates  the  strict  canons  by  which  so  many  submit  to  be  fettered,  and  showing  the 
advantages  thereby  secured. 

3.  For   the    guidance    of    the    workman,  there    are    required    detail  drawings,    showing 
the     construction     of    the     different     parts,     and     a    general   plan,     showing     these     parts 
assembled,  or   put    together. 

If  a  machine  is  to  be  manufactured  by  the  quantity,  with  interchangeable  parts, 
a  separate  drawing  is  usually  made  of  each  individual  piece,  large  or  small,  with  all 
the  dimensions  accurately  marked  in  figures.  And  the  idea  is  to  some  extent  prevalent 
that  this  is  always  necessary,  and  that  the  draughtsman's  work  is  not  complete  with- 
out it. 

But  the  term  detail  drawing  is  also  used  in  another  sense.  Suppose  the  case  of 
a  constructing  engineer  designing  the  machinery  for  a  steamship.  He  must  furnish  to 
the  building  shop,  certainly,  drawings  from  which  the  engines  can  be  made  as  he 
plans  them,  but  in  his  detail  sheets  he  need  not  dissect  so  minutely  as  above 
indicated.  A  drawing,  for  instance,  of  the  connecting  rod,  showing  it  keyed  together 
as  when  in  place,  is  as  properly  a  detail  drawing  as  though  the  shank,  brasses,  gibs, 
keys,  straps,  bolts  and  set-screws  were  disconnected  and  scattered  broadcast  over  the 
paper.  It  is  indeed  a  better  working  drawing,  since  with  a  fraction  of  the  labor  it 
explains  more,  showing  both  how  the  different  pieces  are  made  and  how  they  are 
related  to  each  other  and  fitted  together. 

4.  It     is     in    this    broader   sense     that    we     use     the     expression    detail    drawings,    as 
distinguished     from     what     might     more     accurately     be    called     the     detached    drawings 
mentioned    above.     The    former    are    always    necessary,    whether   the    others   are    required 
or   not ;    he    who    can    make    them    can    always    make    the    others    on    occasion ;    and    the 
more  skilfully  he  can  make  them, — the  greater  his    ability  to    condense,  and    to  reduce  the 
number  of  sheets, — the  more  efficient  will  he  be,  and  the  more  expeditiously  can  he  "  put 
work  in  hand  "  in  cases  of   emergency.     They  are    in    effect    both  "  general "  and  "  detail  " 
drawings  for  the  members  of    the  machine,  and  are    all  that  the    designer   need   furnish  to 
the  constructor,  who  is  at  liberty  to  follow    his  own    judgment    as    to    further   subdivision. 

5.  General    plans,  as   above    stated,    are    intended    to    show    how    the    various    parts   of 
the    machine    are    arranged    and    put    together   as    a    whole. 

They  are  too  often  made  upon  the  assumption  that  in  each  view  it  is  necessary 
to  introduce  every  piece  that  would  be  visible,  partially  or  wholly,  in  the  corresponding 
view  of  the  machine  itself.  The  effect  is  sometimes  more  confusing  than  explanatory, 
and  in  the  majority  of  cases  a  great  many  minor  details  can  be  omitted  not  only 
without  detriment,  but  with  a  great  gain  in  perspicuity.  This  is  more  especially 
true  as  to  bolts  and  nuts — the  fastenings  must  of  necessity  be  shown  in  the  detail 
drawings,  and  usually  a  repetition  of  them  is  worse  than  useless. 

6.  No    rule    can    be    laid    down    as    to    how    many    views   should    be    made,    or   what 
views    they    should     be ;     these    points    must    be    decided     by    common-sense    and     good 
judgment,  aided    by   experience.      But    there    can    be    no    greater    mistake    than    the    too 
common    deduction    from    a     study    of    projections,    that    a    front    view,    an    end    view    and 
a   top    view    are    always    required    and    always    sufficient.     No    pains    should    be    spared    to 


WORKING   DRAWINGS  DEFINED.     RULES  OF  PROJECTION  DEFIED.       3 

make  drawings  clear,  and  the  meaning  unmistakable :  this  must  be  done  at  any  cost, 
but  all  beyond  that  is  superfluous  and  a  waste  of  time.  If  one  view  will  answer  the 
purpose,  so  much  the  better ;  but  if  a  dozen  are  necessary,  they  must  be  made. 
Before  sending  out  a  sheet,  let  the  draughtsman  satisfy  himself  that  the  representations 
and  annotations  are  such  that  by  following  them  the  workman  can  make  what  is 
intended,  and  cannot  make  anything  else ;  then,  and  not  until  then,  his  working  drawing 
is  complete ;  and  in  a  practical  sense  correct,  no  matter  how  numerous  or  flagrant 
the  violations  of  theoretical  formality. 

7.  As    before    intimated,    it     is    not     easy    to    frame     a     definite     code     of    laws     for 
guidance    in    breaking    those    of    another   code ;    because    the   circumstances   which    justify 
the   breaking   of   any   one    may   vary   in    different    cases.     But    it    is   possible   to   indicate 
some,  at   least,  of   the  articles   of   that   code,  the   ignoring   of  which   is   likely  to   be  most 
frequently   recommended.      Among   these   are   the   following : 

(1)  That   all    the    things    shown    in    any   drawing    must    be    represented    in    all    the 
different   views,  as   preserving   the   same   absolute   and    relative   positions. 

(2)  That    everything  visible   in  one  view  of   a  drawing,  must  also   be   shown   in  every 
other   view. 

(3)  That    in   sectional   views  the   cutting   plane   should   be   parallel   to   the   paper. 

(4)  That    everything   should    be    shown    in    section,    through    which    the    cutting    plane 
in    a   sectional    view    would    pass    if    indefinitely    extended. 

(5)  That    everything   beyond    a   cutting    plane    should    be    shown. 

8.  And    in    opposition    to    these    in    their    order,    the    following    general    principles 
may   be    enunciated  : 

(1)  That    in   each    separate    view,  whatever    is  shown    at    all    should  be    represented    in 
the    most    explanatory   manner. 

(2)  That    which    is    not    explanatory    in    any   one    view  may    be    omitted    therefrom,  if 
sufficiently   defined    in    other   views. 

(3)  The    proper    position  of   a    cutting  plane  is    that    by    which    the    most    information 
can   be   clearly   given. 

(4)  It    is   not    necessary    to    show    in    section    everything    which    might    be    divided    by 
a    cutting  plane. 

(5)  Whatever    lie.-;    beyond    a    cutting    plane    may    be     omitted    when    no     necessary 
information    would    be    conveyed    by    its    representation. 

9.  In    what    follows,  no    attempt    has    been     made    to    observe    the    above    order    in 
arranging   the    illustrative    examples.     That    could    not  well    be    done,  for   the    reason    that 
in    many   of   them    more    than    one    of    these    principles    is    involved,  as    well    as    others    of 
less    moment    not    here    enumerated.     They    are    accordingly   given,  rather    in    the    order 
of    the     relative     importance     of     the     special     methods     of     representation    which     are 
recommended. 

And  these,  it  is  proper  to  say,  are  such  as  have  not  only  received  the  sanction 
of  the  highest  authorities,  but  have  stood  the  test  of  trial  and  of  use ;  for  they  have 
been  continuously  employed,  during  years  of  practice,  in  the  preparation  of  drawings 
from  which  machinery  to  the  value  of  many  millions  has  been  constructed. 


PRACTICAL    APPLICATIONS    OF    THE     FOREGOING    PRINCIPLES. 


EXAMPLE    I. 

10.  We   select   as   the   first  -subject    for   illustration,   an    upright   cylinder   fitted    with 
a   cover.     A  vertical  section  of   both,  and  a   top  view  of   the   cover,  are    given    in    Fig.   I. 

Let  it  be  noted,  first,  that  in  the  top  view  the  bolt-holes  only  are  shown,  the 
nuts  being  omitted. 

The  section  is  by  the  plane  ab  through  the  axis ;  which  passes  through  a  bolt 
at  d  on  the  right,  and  midway  between  the  bolts  c  and  e  on  the  left. 

But  it  is  to  be  noted,  secondly,  that  the  sections  of  both  cylinder  and  cover  are 
made  continuous,  as  though  there  were  no  bolts,  and  the  bolts  themselves  are  then 
dotted  in  ;  and,  thirdly,  that  on  each  side,  the  centre  line  of  the  bolt  is  placed  at 
its  actual  distance  from  the  edge  of  the  flange. 

11.  One    important    precept  is  here    illustrated,  an  exception    to  which    is  very  rarely 
met    with,   viz.:     The    continuity    of     masses    of    metal    should    not    be    broken   for    tlie 
purpose   of  showing  fastenings. 

In  this  example,  the  conveying  of  the  idea  of  the  construction  as  a  whole 
depends  more  upon  showing  at  a  glance  the  thickness  and  the  breadth  of  each 
flange,  than  upon  any  other  one  thing. 

The  cylinder  and  the  cover  must  be  fastened  together,  and  the  bolts  are  made 
for  that  purpose ;  but  being  subordinate,  they  should  not  be  made  unduly  prominent. 

A  very  common  and  very  faulty  method  of  drawing  the  sectional  view  in  such 
cases  is  shown  at  A,  upon  which  the  makers  insist,  because,  they  say,  the  bolt  lies  in 
the  plane  of  the  section. 

But  the  effect  is  very  much  as  though  the  bolt  thus  brought  into  notice  were  the 
important  feature,  and  the  cylinder  and  its  cover  made  chiefly  for  the  purpose  of  using 
it.  Still  worse,  two  little  portions  of  the  flanges  are  thus  isolated,  like  islands  lying 
off  a  headland,  and  the  main  idea  is  neither  as  clearly  nor  as  forcibly  expressed  as  it 
is  in  the  method  recommended,  while  the  labor  is  greater. 

Again,  it  is  very  common  to  see  the  nuts  carefully  drawn  in  the  top  view ;  and 
projected  to  their  corresponding  positions  in  the  side  view,  as  also  shown  in  A.  The 
whole  of  this  is  a  sinful  waste  of  time.  If  the  kind  of  bolt,  its  size,  its  true  position  in 
the  flange,  and  the  form  of  the  nut,  are  shown  in  the  section,  there  is  no  use  of  showing 
the  projections  of  the  nuts  beyond  the  plane  of  the  section ;  and  if  the  number  and 
arrangement  of  the  bolt-holes  is  shown  in  the  top  view,  there  is  no  use  of  drawing  the 
nuts. 

12.  A  vast  amount    of    time    and   labor   are  in  many  cases  worse  than  wasted  in  just 


PRACTICAL   APPLICATIONS.  5 

such  apparently  small  items  as  these;  and  we  wish  to  impress  upon  the  reader  this 
maxim,  tliat  each  view  should  be  made  to  tell  all  it  can,  but  nothing  sliould  be  put  in  it 
which  does  not  tell  something  worth  knowing. 


FIG.  i. 


Another  illustration  of  the  disadvantage  of  giving  too  great  prominence  to  the 
fastenings  is  given  in  Fig.  2,  which  shows  one  arrangement  of  a  double-riveted  joint 
between  two  sheets  of  wrought-iron.  If  the  rivets  are  shown  in  full,  each  sheet  is  cut 


PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 


into  three  detached  parts  in  the  sectional  view,  and  the  extent  of  the  lap,  which  is  the 
feature  of  prime  importance,  instead  of  being  made  to  catch  the  eye  at  the  first  glance, 
is  thrown  quite  into  the  shade,  and  requires  a  little  mental  arithmetic  for  its  full 
realization. 


V 


V 


7 


\ 


V 


FIG.  2. 

It  must  also  be  recollected  that  in  studying  a  drawing,  the  designer  himself  will  find 
it  greatly  to  his  advantage  if  the  relative  proportions  of  the  parts  are  made  as  conspicu- 
ous as  possible:  and  in  the  representation  of  bolted  or  riveted  joints  nothing  could  be 
devised  which  would  make  them  less  conspicuous  than  to  cut  the  joined  pieces  into  little 
bits,  in  the  style  here  condemned. 


EXAMPLE    II. 


13.  In  Fig.  3  is  shown  a  vertical  cylindrical  box,  divided  transversely  for  a  part  of 
its  depth  by  a  web  upon  which  are  formed  two  hubs,  through  which  bolt-holes  pass,  and 
provided  with  four  lugs  perforated  for  holding-down  bolts. 

In  the  top  view  the  lugs  are  disposed  diagonally  with  reference  to  the  main  centre 
lines ;  this  being  the  position  which  the  piece  is  to  occupy  when  in  place.  In  order  to 
show  the  true  diameter  and  thickness  of  the  cylinder  in  the  section,  the  cutting  plane 
should  pass  through  ab:  in  that  case  it  would  also  cut  the  dividing  web. 

And  too  often  the  position  is  meekly  accepted,  the  web  cut  through  and  the  outlines 


PRACTICAL    APPLICATIONS. 


FIG.  3. 


8  PRACTICAL  HINTS  FOR  DRAUGHTSMEN. 

of  the  bolt-holes  drawn  in,  separating  the  mass  into  three  parts;  and  to  cap  the  climax 
the  lugs  are  projected  and  dotted  in,  with  all  the  obscurity  attendant  thereupon.  As  a 
good  specimen  of  bad  judgment,  and  as  a  warning  to  the  reader,  all  these  enormities . are 
represented  in  section  A. 

The  proper  course  is  to  back  the  bull  off  the  bridge,  in  all  similar  cases.  The  true 
diameter  and  thickness  arc  shown  in  the  section,  but  an  outside  view  of  the  web  and  its 
hubs  is  given,  as  though  they  were  beyond  the  cutting  plane.  Moreover,  the  lugs  are 
shown  in  external  elevation,  just  as  though  the  line  cd  were  turned  around  the  axis  so 
as  to  coincide  with  ab;  thus  the  centre  line  of  the  lug-bolt  is  shown  at  its  true  distance 
from  the  axis. 

And  the  result  is,  that  in  spite  of,  or  rather  by  reason  of,  these  discrepancies  between 
the  views  considered  as  studies  of  projection,  a  much  clearer  idea  of  the  structure  is 
conveyed  by  the  sectional  view,  while  the  relative  positions  of  the  different  parts  is  shown 
in  the  top  view,,  so  that  with  the  two  before  him  the  workman  cannot  find  an  excuse 
for  an  error. 

It  may  be  stated  as  a  general  rule,  then,  that  a  zueb  parallel  to  the  paper  should  not 
be  shown  in  section,  even  though  a  plane  cutting  other  parts  which  must  be  so  shown, 
should  be  so  situated  as  to  pass  through  the  web. 

EXAMPLE    III. 

14.  Fig.  4  represents  a  portion  of  a  horizontal  cylinder  upon  the  lower  part  of  which 
is  cast  a  supporting  bracket.  This  bracket  consists  of  a  foot-plate,  connected  with  the 
cylinder  by  two  vertical  webs  at  right  angles  to  each  other.  At  the  end  of  the 
cylinder  a  hub  //  is  formed,  which  is  drilled  and  tapped  for  a  dram-cock. 

This  example  illustrates,  as  did  the  preceding  one,  the  maxim  just  laid  down,  for 
the  vertical  plane  xy  really  cuts  through  both  the  hub  H  and  the  longitudinal  web  of  the 
bracket ; — but  neither  is  shown  as  being  cut,  in  the  longitudinal  section. 

The  form  of  the  foot-plate,  and  the  positions  of  the  holding-down  bolts,  are  clearly 
shown  by  a  horizontal  section  through  ab,  placed  directly  under  the  bracket.  Similarly, 
the  form  of  the  hub  is  shown  by  a  section  through  cd. 

Again,  the  transverse  cutting  plane  ws  is  so  situated  as  actually  to  split  the  central 
cross  web,  which  accordingly  is  not  drawn  in  section. 

Notice  is  also  to  be  taken  of  the  fact  that  since  the  hub  H  is  fully  explained  by 
the  two  views  of  it  above  mentioned,  it  is  not  dotted  in  behind  the  bracket  in  the  trans- 
verse section,  although  the  cylinder  flange  is.  This  flange  is  thus  shown,  not  so  much 
because  it  is  necessary  in  order  to  define  its  form,  as  for  the  purpose  of  exhibiting  the 
arrangement  of  the  bolt-holes ;  there  being  a  bolt  on  the  vertical  centre  line,  opposite  the 
hub,  the  hole  for  it  must  be  tapped,  as  indicated  by  dotting  two  circles,  one  for  the 
bottom  and  the  other  for  the  top  of  the  thread. 

This  being  an  important  consideration,  and  a  thing  which  could  not  be  otherwise 
shown  in  these  views,  affords  another  reason  for  omitting  the  representation  of  the  hub, 
which  if  introduced  here  would  obscure  this  bolt-hole  by  the  confused  mass  of  dotted 
lines. 


PRACTICAL   APPLICATIONS. 


io  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 

EXAMPLE     IV. 

15.  The  next  illustration,  Fig.  5,  is  that  of  a  simple  pulley  or  drum,  consisting  of  a 
rim  connected  with  the  hub  by  a  web,  and  secured  upon  the  shaft  by  a  key. 

In  the  end  view,  the  shaft  and  key  are  brought  out  most  distinctly  by  showing  them 
in  section,  as  though  cut  off  flush  with  the  end  of  the  hub  by  the  transverse  plane  ab. 

The  other  view  is  in  the  main  a  section  by  the  plane  xy.  The  shaft,  however,  is 
not  shown  as  cut  through,  nor  do  we  think  it  ever  would  be  unless  it  were  hollow,  as  is 
sometimes  the  case,  or  possessed  some  other  peculiar  feature  which  would  call  for  such  a 
course. 

But  it  is  to  be  noticed  that  this  drawing  shows  the   key  dotted  in   as    though    it  lay 


FIG.  5. 

beyond  the  cutting  plane.  A  very  common  fault  is,  to  draw  the  upper  part  of  the  key, 
which  is  outside  the  shaft,  in  full,  as  well  as  the  shaft  itself. 

In  that  case  the  sectioning  of  the  upper  half  of  the  hub  terminates  at  the  upper 
outline  of  the  key ;  and  the  effect  is  that  the  whole  appears  lop-sided,  as  though  the 
hub  were  eccentric,  or  thinner  on  one  side  than  on  the  other. 

It  may  be  urged  that  this  can  lead  to  no  error,  since  all  is  explained  by  the  end 
view.  The  truth  of  this  argument  we  freely  admit ;  but  there  can  be  no  good  reason 
why  that  false  impression  should  be  conveyed  by  either  view. 

And  we  shall  have  occasion  to  illustrate  in  other  examples  the  maxim,  which  is  of 
no  small  moment  sometimes,  that  if  a  thing  be  symmetrical,  it  should  be  represented  as 
symmetrical  in  every  vieiv  if  possible. 


PRACTICAL   APPLICATIONS.  n 

EXAMPLE    V. 

16.  Fig.  6  shows  two  hand-wheels,  one  having  four  straight  arms,  the  other  three 
curved  ones. 

It  is  particularly  to  be  noticed  that  the  longitudinal  section  is  the  same  for  both, 
and  if  xy  be  regarded  as  the  cutting  plane,  it  does  not  represent  the  appearance  of 
either.  But  it  does  show  exactly  what  the  workman  wants  to  know,  viz.,  the  forms  of 
the  sections  of  the  rim  and  of  the  hub,  the  thickness  of  the  arms  at  the  hub  and  at 
the  rim,  and  the  sizes  of  the  side  fillets  at  the  ends  of  the  arms.  In  the  case  of 
the  wheel  with  the  three  curved  arms,  a  true  section  by  the  plane  xy  would  show  the 
upper  side  of  the  rim  and  of  the  hub  with  an  unsightly  and  unsymmetrical  excrescence, 
which,  if  not  unintelligible  as  well,  would  at  best  convey  no  information  except  that  the 


FIG.  6. 

draughtsman  knew  how  to  make  the  section :  and  the  same  may  be  said  of  the  fore- 
shortened projection  of  the  lower  arm  and  its  junction  with  the  rim. 

In  the  case  of  the  other  wheel,  a  true  section  by  the  plane  xy  would  at  first  glance 
convey  the  impression  that  hub  and  rim  were  joined  by  a  continuous  web.  Closer  study 
would  rectify  the  error  if  the  outlines  of  the  hub  and  the  rim  were  completed  by  dotted 
lines :  still,  that  is  not  a  good  reason  for  making  a  drawing  which  can  possibly  convey 
such  an  idea,  when  it  is  easier  to  make  one  which  can  not. 

17.  The  form  of  the  arms  is  explained  by  making  a  transverse  section  of  one  of 
them,  as  by  the  plane  ab :  this  section  should,  as  shown,  be  drawn  at  one  side  of  the 
arm,  and  not  direct!}"  upon  it.  as  is  sometimes  done;  a  device  apparently  founded  on 
the  idea  of  "  revolving  the  cutting  plane  about  its  trace  into  the  plane  of  projection," 
but  a  very  ineligible  one :  for  it  has  precisely  the  appearance  which  would  and  should  be 
presented  if  the  arm  had  a  piece  cast  upon  it,  projecting  from  the  front  side — such  a 
piece  could  not  be  more  effectively  brought  into  notice  than  by  sectioning  it. 


iz  PRACTICAL  HINTS  FOR   DRAUGHTSMEN. 

The  fact  that  the  arms,  by  reason  of  their  thickness,  do  not  join  the  rim  entirely 
on  the  inner  circumference,  but  encroach  upon  its  breadth,  is  indicated  in  the  front 
views  by  the  curves  cd. 

These,  it  is  to  be  observed,  are  not  curves  of  intersection  properly  so  called,  but 
indicate  the  lines  of  tangency  of  the  fillets  formed  at  the  ends  of  the  arms  and  the 
surface  of  the  rim. 

Strictly,  then,  they  are  imaginary  lines,  and  some  worshippers  of  the  Correct  insist 
that  they  ought  not  to  be  drawn.  But  such  evidences  of  things  not  seen  will  often 
define  most  clearly  the  substance  of  things  hoped  for:  and  when  they  will  it  may  be  as 
well  to  let  them.  In  the  present  instance,  and  in  others  which  will  be  met  with  subse- 
quently, it  is  beyond  dispute  that  the  introduction  of  these  imaginary  lines,  if  drawn 
finely,  is  fully  warranted  by  the  service  they  render  in  making  the  drawing  intelligible. 

EXAMPLE    VI. 

18.  Fig.  7  represents  a  crank,  crank-pin,  and  a  portion  of  a  shaft,  including  a  journal 
between  two  collars  formed  upon  the  shaft. 

This  is  introduced  here  in  further  illustration  of  the  use  of  imaginary  lines,  as  being 
a  case  in  which  they  are  absolutely  essential. 

It  is  a  well-known  fact  that  if  a  crank-pin  of  the  form  here  shown  be  made  with  a 
sharp  corner  at  the  inner  face  ab,  like  that  at  the  outer  face  cd,  it  will  be  very  liable  to 
break  there ;  and  that  the  same  is  true  if  the  junction  of  the  shaft  with  the  collars  be 
made  sharp,  even  if  the  angle  be  a  right  angle. 

The  liability  to  accident  is  very  greatly  reduced  by  rounding  out,  or,  as  it  is  called, 
"  filleting,"  these  angles,  as  shown  in  the  drawing,  the  vertical  lines  being  joined  to  the 
horizontal  ones  by  quarter-circles. 

If,  as  often  happens,  circumstances  prevent  the  use  of  a  long  journal,  it  becomes 
necessary,  in  order  to  secure  as  much  cylindrical  bearing  surface  as  possible,  to  make  the 
fillets  as  small  as  may  be ;  and  very  small  ones  are  far  better  than  none  at  all. 

In  such  a  case,  especially  if  the  drawing  be  on  a  small  scale,  the  very  existence  of 
the  fillet  might  be  overlooked,  were  the  line  of  tangency  not  drawn  in.  This  renders 
such  an  oversight  impossible,  no  matter  how  fine  the  line ;  and  the  finer  it  is  the  better 
the  drawing  will  look. 

Tastes  differ  in  regard  to  the  question  whether  this  addition  improves  the  appearance 
of  a  drawing ;  but  the  draughtsman  whose  experience  includes  the  breaking  of  a  shaft 
in  consequence  of  its  omission,  will  thereafter  vote  in  the  affirmative :  the  safe  side  is 
always  the  most  comfortable. 

It  may  then  be  stated  that  in  general,  though  the  rule  has  exceptions,  the  fillet  lines 
sliould  be  drawn  in  outside  vicivs  of  surfaces  of  revolution. 

This  crank  is  shown  as  secured  to  the  shaft  by  two  keys,  the  positions  of  which  are 
shown  in  the  end  view,  which  also  defines  the  cross-section  of  the  keys.  The  side  view 
can  convey  no  further  information  except  as  to  the  length  of  the  keys ;  and  this  is  as 
well  done  by  showing  only  one  of  them,  while  it  is  clearer  to  place  it  in  that  view  at  the 
top  of  the  shaft,  which  is  accordingly  done. 


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o 
£    . 


i4  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 


EXAMPLE    VII. 

19.    A  simple  pillow-block,  consisting  of  bed,  cap,  and  bolts,  without  brasses.     Fig.  8. 

This  example  illustrates  chiefly  the  selection  of  views.  An  end  view  of  a  pillow- 
block  is  often  made,  in  addition  to  those  given  :  but  if  it  be  in  elevation,  its  only  effect 
is  to  consume  time  in  the  drawing  office  without  saving  it  in  the  shop.  In  pillow-blocks 
of  more  complicated  construction,  particularly  if  the  brasses  be  hollow,  or  babbitted,  or 
both,  a  longitudinal  section  may  advantageously  be  added ;  in  which  case  it  is  to  be 
observed  that  the  dotting  in  of  parts  beyond  the  plane  of  section,  and  concealed,  is  better 
omitted. 

In  the  present  instance,  the  side  and  the  top  view  are  all  that  are  required.  And  in 
the  latter,  only  the  bed  is  shown ;  the  cap  and  the  bolts  are  removed. 

It  is  sufficiently  indicated  by  the  lines  in  the  side  view,  that  the  form  of  the  cap 
corresponds  to  that  of  the  top  of  the  bed ;  and  the  bolts,  with  their  heads  and  nuts, 
are  fully  denned  in  that  view.  By  leaving  these  things  out  in  the  top  view,  we  not 
only  save  the  time  that  would  be  occupied  in  drawing  them,  but  make  the  view  clearer; 
as  the  form  of  the  pocket  in  -which  the  head  of  the  bolt  is  buried,  must  be  dotted  in 
at  any  rate,  which  could  not  consistently  be  done  without  dotting  in  also  the  head  of 
the  bolt,  and  over  this  again  would  come  the  full  outline  of  the  nut.  The  effect,  as 
a  moment's  consideration  will  show,  would  be  to  confuse  this  part  of  the  work  by  super- 
position of  lines.  Judicious  omission  is  preferable  to  correct  superfluity. 


EXAMPLE    VIII. 

20.  An  ornamental  air-vessel,  with  an  opening  in  the  top,  into  which  is  screwed  the 
plug  P.  This  plug  is  itself  bored  out  and  tapped  for  the  insertion  of  the  pipes  T,  T. 
Fig.  9. 

This  exhibits  a  legitimate  expedient  for  combining  the  advantages  of  a  sectional  view 
and  an  elevation.  The  general  appearance  and  proportions  of  the  air-chamber  are  best 
shown  by  an  outside  view,  but  the  form  of  the  interior,  and  the  arrangement  of  the  plug 
and  pipes,  if  merely  dotted  in,  would  not  be  as  distinctly  seen  as  if  drawn  in  section. 
The  body  and  neck  of  the  vessel  are  round ;  the  bottom  flange  is  square,  as  indicated  by 
the  shadow  lines. 

In  sectioning  over  an  outside  view  in  this  manner,  the  section  lines,  or  cross-hatching, 
should  be  full,  and  not  dotted  or  broken  ;  the  effect  of  this  last  is  simply  to  make  a  confused 
mass  of  dots,  while  the  effect  which  sectioning  should  have  is  that  of  a  light  tint,  not 
heavy  enough  to  overpower  the  outlines. 

Dotted  parallel  lines  which  are  close  together  have  in  all  cases  a  very  unpleasing  and 
indistinct  effect.  In  order  to  avoid  this  in  representing  the  tube  T,  it  is  to  be  noted 
that  the  external  outlines  only  are  shown,  except  at  the  lower  part.  Here  a  section  of 
the  pipe  is  made,  in  full  lines,  just  as  though  a  portion  of  the  wall  of  the  air-chamber 
had  been  broken  out,  thus  permitting  the  pipe  to  be  seen.  The  actual  execution  of  that 


PRACTICAL  APPLICATIONS. 


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PRACTICAL  HINTS  FOR  DRAUGHTSMEN. 


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FIG.  g. 


PRACTICAL   APPLICATIONS. 


process  is  sometimes  shown,  by  making  a 
broken  line  representing  the  fracture ;  but 
in  such  cases  as  this,  it  would  merely  be 
hideous  without  any  compensating  advan- 
tage. 

EXAMPLE    IX. 

21.  A  vertical  shaft,  Fig.  10,  upon 
which  is  pinned  a  collar  C,  supporting  a 
piece  B  which  turns  freely  on  the  shaft. 

This  again  illustrates  the  advantage 
sometimes  gained  by  sectioning  over  an 
outside  view.  Both  B  and  C  are  of  such 
form  that  outside  views  of  them  are 
needed,  or  at  least  best  suited  to  the  cir- 
cumstances. But  an  outside  view  only  of 
these  three  pieces  in  place  would  be  am- 
biguous, since  it  would  appear  exactly  the 
same  were  B  and  C  made  in  one  piece. 
This  ambiguity  is  entirely  removed  by 
sectioning  over  the  outlines,  which  never- 
theless explain  the  outward  forms  just  as 
clearly  as  if  it  were  not  done. 

A  very  common  but  very  objection- 
able practice  in  such  cases  as  this  is  to 
make  an  end  view  also,  showing  all  the 
pieces  in  place :  with  the  result  of  show- 
ing nothing  clearly.  The  only  reasonable 
method  is  to  make  an  end  view  of  each 
piece  by  itself,  as  in  the  figure :  though  in 
the  case  of  the  collar,  C,  it  may  be  rather 
an  advantage  than  otherwise  to  show  the 
shaft  within  it,  if,  as  is  here  done,  it  be 
drawn  in  section. 

And  in  general,  it  is  to  be  recollected, 
the  fact  that  in  one  view  a  number  of 
parts  are  shown  as  put  together  is  not  a 
sufficient,  and  often  is  not  even  a  good, 
reason  for  preserving  that  arrangement  in 
other  views, — in  which  they  should  be 
separated  if  that  shows  them  more  clearly. 


FIG.  10. 


iS 


PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 


PRACTICAL   APPLICATIONS. 


EXAMPLE   X. 

22.  A  rock-shaft,  with  two  levers  which  are  not  in  line  with  each  other,  is  shown  in 
Fig.  n. 

• 

This  combination  differs  from  the  preceding  in  the  particular,  that  no  confusion  is 
caused  by  superposition  of  lines  in  the  end  view,  although  the  parts  are  there  shown  as 
put  together ;  which  indeed  is  necessary  in  order  to  define  the  relative  position  of  the 
two  levers. 

This  is  best  done,  as  shown,  by  placing  one  of  them  so  that  its  centre  line  is  vertical, 
as  cd ;  the  side  view  of  that  one  will  then  correspond  to  it  as  a  true  projection.  The 
centre  line  of  the  other  lever  is  drawn  in  the  end  view  at  the  correct  angle  with  that  of 
the  first ;  which  angle  is  best  defined  on  the  drawing  by  describing  an  arc,  ab,  through 
the  centre  of  the  second  pin,  about  c,  the  axis  of  the  rock-shaft,  and  marking  in  figures 
either  the  length  of  the  chord  ab,  or  else  the  offset,  or  horizontal  distance  of  b  from  cd, 
or  both. 

But  in  the  side  view  the  formation  of  this  second  lever  is  best  shown,  not  by  pro- 
jecting it  in  its  inclined  position,  but  by  drawing  it  as  though  it  also  were  vertical. 
Thus  the  true  dimensions  are  seen  in  both  vifzus;  which  is  essentially  more  explanatory 
than  it  is  to  exhibit  the  same  relative  position  of  parts  in  both  views,  whenever,  as  is 
the  case  here,  some  parts  would  thereby  be  foreshortened. 


FIG.  12. 

EXAMPLE  XI. 

23.  A  simple  link  with  a  jaw  at  each  end,  Fig.  12.  The  pin  at  one  end  is  slotted 
for  a  screw-driver,  that  at  the  other  end  being  a  tap-bolt. 

The  tap-bolt  being  intended  solely  to  serve  the  purpose  of  a  pin,  must  neither  bind 
the  jaw  nor  be  liable  to  work  loose.  Its  head  must  therefore  not  touch  the  outside  of 
the  jaw,  and  accordingly,  in  the  side  view,  it  is  limited  by  a  line  just  far  enough  from 
the  jaw  to  show  daylight  between  them.  And  that  it  may  stay  in  place,  the  thread 
bottoms,  just  as  in  the  case  of  a  standing  bolt;  as  shown  by  the  abrupt  termination 


2O 


PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 


are   shown 
Now, 


in 
if   a 


of  the  thread  at  the  face  of  the 
jaw.  The  hexagonal  form  of 
the  head  being  fully  shown  in 
the  side  view,  the  pin  is  best 
shown  in  the  other  view  in  sec- 
tion, as  though  cut  off  flush 
with  the  jaw. 

The  other  pin  also  must  be 
screwed  in  till  the  thread  bot- 
toms :  in  the  side  view  the  true 
size  of  the  slot  is  shown ;  that 
is  to  say,  the  slot  is  supposed 
to  be  perpendicular  to  the  paper, 
as  it  always  should  be,  for  the 
simple  reason  that  it  thus  shows 
more  clearly  what  is  intended. 
In  the  other  view  it  should  be 
placed  in  whatever  position  will 
make  it  most  conspicuous.  Just 
what  that  position  is,  may  de- 
pend upon  circumstances  ;  if  pos- 
sible to  avoid  it,  the  sides  of 
the  slot  should  not  be  parallel 
to  either  centre  line, — and  in 
this  case  they  are  drawn  at  an 
angle  of  45°  to  each. 


EXAMPLE  XII. 

24.  A  stuffing-box,  with  gland 
and  bolts,  Fig.  13.  This  stuff- 
ing-box is  cast  as  part  of  the 
cylinder-head  A,  and  has  a  cir- 
cular flange  B,  in  which  are 
fixed  two  standing  bolts,  which 
pass  through  lugs  formed  on 
the  gland. 

This  drawing  is  made  on 
principles  in  direct  opposition 
to  those  of  strict  projection. 
In  the  first  place,  the  cylinder- 
head  and  the  stuffing-box  itself 

complete   section,  the   standing   bolts   being   drawn   as   in    Ex.    I. 

true   section    were    made    by    the    plane   xy   through    the    gland,    (which    is 


PRACTICAL   APPLICATIONS.  21 

too  often  perpetrated,)  no  one  could  tell,  by  looking  at  that  section,  but  that  the 
gland  itself  had  a  large  circular  flange,  as  well  as  the  stuffing-box,  which  might  very 
easily  be,  and  often  is,  the  case.  But  here,  the  gland  is  furnished  only  with  two  lugs, 
which  toward  the  centre  spread  out  and  merge  into  a  stiffening  ring,  or  narrow  flange, 
formed  at  the  outer  end  of  the  gland. 

That  this  may  be  distinctly  kept  in  view  even  while  examining  the  sectional 
drawing,  the  lug  is  there  shown  in  elevation,  while  the  body  of  the  gland  is  shown 
as  though  a  section  by  the  plane  mn  were  turned  about  the  axis  into  the  plane  of 
the  paper. 

And  it  should  be  shown  in  the  same  way  exactly,  whether  the  bolts  are  actually  on 
the  vertical  line  or  not ;  the  required  position  of  the  gland  being  shown  in  the  end  view. 

EXAMPLE  XIII. 

25.  A  valve  and  valve-seat  for  a  water-pump,  Fig.  14.  The  valve  consists  of  an 
india-rubber  disk  into  which  is  sprung  a  central  eyelet  of  brass,  bored  out  to  slide 
freely  on  a  sleeve  which  supports  the  valve-guard  that  limits  the  lift  of  the  valve  ;  the 
whole  being  held  in  place  by  a  bolt  passing  through  the  sleeve  and  guard,  and  also 
through  the  central  hub  of  the  seat. 

We  have  here  another  case  in  which  the  sectional  view  is  constructed,  not  to  ex- 
hibit a  knowledge  of  projections,  but  to  convey  information  by  any  means  which  will  do 
it  clearly. 

The  valve-seat  is  a  grating,  circular  in  outline  and  having  a  central  hub  from  which 
arms  radiate,  as  shown  in  the  top  view,  where  everything  relating  to  the  thickness  and 
arrangement  of  the  arms,  the  form  and  dimensions  of  the  openings,  etc.,  is  made  evi- 
dent at  a  glance. 

A  second  glance  makes  it  equally  evident  that  the  regular  proceeding  dictated  by 
the  laws  of  projection,  that  is  by  making  a  vertical  section  through  the  plane  xy,  would 
make  the  other  view  very  unsatisfactory  and  actually  misleading :  nor  in  fact  is  there 
any  one  plane  which  can  be  so  passed  as  to  render  a  true  section  by  it  very  ex- 
planatory. 

Accordingly,  the  sectional  view  is  constructed  as  follows :  the  bolt  is  first  drawn 
with  the  flat  side  of  the  square  head  parallel  to  the  paper ;  the  exterior  lines  of  the 
hub  are  then  drawn,  so  as  to  show  its  true  diameter,  next  the  inside  and  outside  lines 
of  the  central  ring  of  the  grating,  in  which  the  inner  arms  terminate,  then  the  inside 
line  of  the  outer  ring ;  thus  the  outer  part  only  of  this  view  is  a  "  correct"  section,  such 
as  is  insisted  on  by  extreme  advocates  of  order  and  system.  But  //  tells  its  story,  and 
tells  it  more  truly  than  it  can  be  told  by  calvinistic  observance  of  the  letter  of  the  law. 
The  end  justifies  the  means. 

It  is  so  obvious  from  these  two  views  that  the  rubber  valve  is  round,  and  also  the 
eyelet  and  the  sleeve,  that  it  would  be  ridiculous  to  make  end  views  of  those  pieces  in  a 
working  drawing.  A  top  view  of  the  guard  would  be  necessary — which  is  not  here  given, 
as  the  object  of  the  illustration  is  simply  to  call  attention  to  the  manner  in  which  the  sec- 
tional view  is  constructed. 


PRACTICAL   HINTS. FOR   DRAUGHTSMEN. 


1 


FIG.  14. 


PRACTICAL  APPLICATIONS. 


FIG.  15. 


24  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 


EXAMPLE  XIV. 

26.  Fig.   15.  A  poppet  valve  and  valve-seat. 

The  valve,  supposed  to  be  of  brass,  is  made  of  a  dished  form  for  strength,  and  cast 
in  one  piece  with  the  stem,  the  lower  part  of  which  serves  as  a  guide  to  insure  correct 
seating  when  the  valve  closes.  Large  fillets  are  shown  at  the  junction  of  the  valve  with 
the  stem  both  above  and  below:  and  as  the  stem  is  best  shown  in  outside  view,  thus 
indicating  its  cylindrical  form  by  the  absence  of  shadow  lines,  the  fillet  lines  are  drawn 
in.  The  body  of  the  valve  is  shown  in  section,  and  the  cross-hatching  is  continued  a 
little  way  upon  the  stem,  merely  terminating  indefinitely  without  a  line  of  fracture  being 
shown. 

The  valve-seat,  also  of  brass,  consists  of  a  cylindrical,  or  rather  very  slightly  taper- 
ing ring,  tightly  driven  into  the  neck  of  the  cast-iron  valve-chamber.  Within  the  ring, 
and  forming  one  piece  with  it,  is  a  spider  of  several  arms,  supporting  a  central  hub 
through  which  the  lower  part  of  the  valve-stem  slides  freely  as  a  guide.  This  seat 
is  also  shown  in  section,  the  two  sides  being  drawn  as  symmetrical,  an  outside  view  of 
one  arm  of  the  spider  being  made  on  each  side  of  the  centre  line,  without  regard  to 
the  actual  number  or  position  of  these  arms.  These  particulars  are  defined  in  the  top 
view,  in  which  the  valve-seat  is  shown  as  cut  by  the  horizontal  plane  ab.  But  this 
plane  is  not  extended  to  cut  the  metal  of  the  valve-chamber ;  for  a  much  clearer  idea 
of  the  general  proportions  is  given  by  cutting  the  cast-iron  neck  by  the  plane  cd. 
In  a  shop  drawing  it  would  not  be  obligatory  to  make  this  top  view  at  all,  since  it 
would  practically  suffice  to  write  upon  the  longitudinal  section  the  instructions  about 
the  spider,  thus :  "  Three  arms,  f"  thick,"  and  also  the  number  of  bolts  in  the  lower 
flange  of  the  chamber. 

EXAMPLE  XV. 

27.  Drawing   of   Spur-Wheels.       Fig.    16. 

A  spur-wheel  if  very  small  may  be  made  by  cutting  teeth  in  a  simple  disk  of 
metal,  as  in  the  change-wheels  of  engine  lathes.  But  large  wheels  usually  consist  of 
an  outer  rim  on  which  the  teeth  are  cut,  connected  to  the  central  hub  by  arms  or  a 
web.  In  general  structure  then  they  closely  resemble  the  pulley  and  the  hand-wheel, 
illustrated  in  Examples  IV  and  V ;  like  them  they  are  best  represented  by  an  end  view 
and  a  longitudinal  section,  and,  as  explained  in  relation  to  them,  this  section  should 
be  made  so  as  of  itself  to  convey  the  impression  of  symmetry. 

In  order  to  this,  the  rim  should  always  be  shown  as  if  cut  between  two  teeth, 
and  the  hub  as  if  cut  between  two  arms,  if  there  be  any,  as  in  the  figure,  without 
regard  to  the  number  or  relative  positions,  which  are  shown  in  the  end  view.  In  the 
larger  of  the  wheels  in  Fig.  16,  the  hub  has  an  external  flange,  and  the  rim  an  in- 
ternal one ;  to  which  the  ribs  of  the  arms  are  joined  by  fillets.  The  section  at  b  b 
shows  the  form  of  the  arm,  as  in  Fig.  6,  and  thus  the  structure  of  the  whole  is 
fully  defined. 

If   time   presses,  it    is   quite   permissible   in    a   shop   drawing   to   draw    only  a   few   of 


PRACTICAL   APPLICATIONS.  25 

the  teeth,  as  in  the  figure ;  this  defines  the  contour,  and  for  the  rest  it  is  sufficient  to 
draw  the  pitch  circle  and  the  outline  of  the  blank,  and  to  mark  in  figures  the  number 
of  teeth  required. 

28.    The   smaller   wheel   is   introduced    for   the   purpose   of   showing    how    two    wheels 
in  gear  with  each  other  are  best  represented  in    section.     If   cut  by  a  single    plane,  which 


FIG.  16. 

would  pass  through  a  tooth  of  one  and  a  space  of  the  other,  the  effect  is  indistinct 
and  misleading.  Instead  of  this,  each  is  cut  through  a  space,  and  the  tooth  of  one  is 
thus  placed  in  front  of  a  tooth  of  the  other;  the  top  of  this  latter  tooth  is  therefore 
dotted,  but  the  bottom  of  the  space  is  shown  in  a  full  line,  thus  making  the  clear- 
ance  obvious  at  a  glance;  and  the  junction  of  face  and  flank  is  indicated  by  drawing 
the  hair  lines  m  m,  which  are  the  outlines  of  the  pitch  cylinders. 


26  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 

The  side  view  of  a  spur-wheel  in  elevation  is  very  seldom  introduced  in  a  detail 
drawing,  as  the  longitudinal  section  usually  answers  every  purpose  as  well  if  not  better, 
and  is  in  any  case  necessary  in  addition  to  the  outside  view  if  the  latter  be  made 
for  any  reason.  Still  it  is  occasionally  desirable,  and  in  a  general  drawing  it  may  be 
necessary :  so  that  a  few  words  in  regard  to  it  are  appropriate. 

And  it  is  to  be  stated,  that  there  is  no  one  thing,  unless  it  be  a  small  screw,  in 
which  the  labor  of  making  a  correct  projection  is  so  absolutely  thrown  away  as  in 
such  an  outside  view  of  a  spur-wheel. 

It  is  utterly  ineffective,  and  it  is  hardly  too  much  to  say  that  the  more  accurate 
it  is,  the  less  will  it  look  like  a  wheel ;  it  will  convey  no  impression  of  roundness,  and 
very  little  of  the  existence  even,  let  alone  the  forms,  of  the  teeth.  This  last,  indeed,  is 
of  little  account,  but  the  drawing,  to  be  of  any  practical  use,  must  at  least  look  round 
and  give  an  idea  that  there  arc  teeth. 

29.  The  manner  in  which  this  may  be  effected  is  shown  at  A  in  the  figure.  Be- 
ginning at  the  side  from  which  the  light  is  supposed  to  come,  lines  are  drawn  par- 
allel to  the  axis,  at  first  as  if  for  shading  a  cylinder  as  large  as  the  blank :  when  this 
has  been  carried  a  small  distance,  the  tops  of  the  teeth  arc  indicated  by  drawing  a 
double  line  for  each,  the  line  away  from  the  light  being  made  a  shadow  line.  The 
breadth  of  the  tops,  and  the  spaces  between  them,  are  slightly  increased  as  they  ap- 
proach the  centre  line,  and  again  gradually  diminished  as  they  recede  from  it  toward 
the  position  of  the  line  of  shade  upon  the  cylinder  of  the  blank,  beyond  which  it  is 
useless  to  continue  the  indication  of  the  tops  of  the  teeth,  unless  for  a  very  little 
distance ;  and  the  remainder  is  finished  as  though  merely  shading  the  cylinder.  Some 
practice,  and  good  judgment,  are  required  to  produce  the  most  satisfactory  effect  in  any 
given  case,  as  the  treatment  must  vary  in  detail  according  to  the  size  of  the  teeth  as 
well  as  the  size  of  the  wheel. 

It  is  to  be  understood  that  this  operation  is  not  for  the  purpose  of  representing 
the  wheel,  in  the  sense  in  which  that  word  is  used  in  general,  and  particularly  in 
treating  of  projections.  No  attempt  is  made  to  make  the  lines  indicating  the  tops  of 
the  teeth  agree  in  number  or  position  with  the  contours  shown  in  the  end  view ; 
and  the  whole  is  to  be  explicitly  considered  as  an  indication  only,  and  not  in  any  sense 
a  drawing,  of  the  wheel. 

If  occasion  arises  to  show  the  side  view  of  two  wheels  in  gear  in  this  manner,  a 
slight  modification  is  necessary,  since  the  cylinders  of  the  blanks  are  not  tangent  to 
each  other ;  on  this  account,  the  above-described  shading  of  that  one  whose  engaging 
side  is  toward  the  light  should  begin  at  a  distance  from  the  axis  equal  to  the  radius 
of  the  pitch  circle.  This  wheel  should  be  first  completed,  and  the  other  one  afterward 
treated  in  the  same  manner:  by  which  the  encroachment  of  one  upon  the  other  due 
to  the  meshing  of  the  teeth  will  be  indicated  in  a  manner  which  will  make  it  intel- 
ligible without  reference  to  the  other  view. 


PRACTICAL   APPLICATIONS.  27 

EXAMPLE  XVI. 

30.  Drawing   of   Bevel   Wheels.     Fig.    17. 

The  sectional  view  shows  two  bevel  wheels  in  gear,  the  smaller  one  cut  out  of 
the  solid,  the  larger  one  of  sufficient  size  to  require  the  web,  which  connects  the  rim 
with  the  hub,  to  be  stiffened  by  ribs.  If  the  wheel  were  larger,  the  connection  would 
be  by  means  of  arms — in  regard  to  the  drawing  of  which  the  same  methods  would  be 
followed  as  in  the  case  of  spur-wheels  and  pulleys. 

The  form  of  the  tooth  is  in  this  case  shown,  not  in  the  end  view  of  the  wheel, 
where  it  would  appear  foreshortened,  but  by  making  a  drawing  by  itself  of  each  end 
of  the  tooth,  as  m,  n.  This  being  done,  the  section  itself  would  suffice  for  a  working 
drawing  if  the  wheel  be  solid  or  have  a  web  only:  and  on  a  pinch  it  would  answer 
when,  as  in  this  case,  ribs  are  added,  if  definite  instructions  be  noted  on  the  section, 
as  for  example  "  Four  radial  ribs,  %"  thick ;"  for  the  shape  of  the  rib  is  defined  in 
the  sectional  view. 

If  arms  are  used,  an  end  view  is  necessary,  and  the  section  of  an  arm  should  also 
be  given  as  in  Figs.  6  and  16.  In  no  case  is  it  necessary  in  the  end  view  to  show 
the  teeth,  a  drawing  of  the  blank  only  being  required  in  order  to  make  the  wheel:  but 
of  course  the  work  looks  more  complete  if  the  teeth  be  drawn. 

In  making  the  section,  the  rim  should  be  cut  between  two  teeth ;  and  the  hub 
between  two  arms  or  ribs,  as  the  case  may  be,  as  previously  explained.  And  in  this 
sectional  view  the  pitch  cones  should  always  be  s/imi'H,  being  drawn  like  the  centre  lines, 
either  hair-lines  if  in  black,  or  a  very  little  heavier  if  in  red  ink  or  other  distinguishing 
color. 

31.  In    a   working   drawing,  it    is    not  advisable  to  draw  the    inner  ends  of    the  teeth, 
which    are    actually    visible    on    the    farther    half    of    the    wheel ;    for    they    would    be    fore- 
shortened,   and   what    is   of   more    consequence,  would    rather   diminish    than    increase   the 
clearness   of    the    drawing :     in     a    general    plan     it    may,    however,  be    desirable    thus    to 
complete    a   wheel    which    may    be    shown    in    section,  particularly    if   other  objects  beyond 
are    partially    concealed    by    it. 

In  regard  to  a  side  elevation  of  a  bevel  wheel,  it  is  to  be  noted  that  since  the 
forms  of  the  teeth  are  actually  shown,  although  foreshortened,  a  true  projection  not 
only  does  convey  a  correct  impression,  but  nothing  else  will :  with  tnis  mitigation,  how- 
ever, of  the  labor  of  making  it,  that  it  is  not  necessary  to  be  rigidly  precise  in  de- 
termining the  contours  of  the  ends  of  the  teeth. 

The  preceding  remark,  it  is  to  be  understood,  relates  to  the  representation  of  the 
wheel  in  outside  view.  In  many  cases  an  indication  will  suffice,  which  is  much  less 
difficult  to  make,  consisting  of  the  frustum  of  the  pitch  cone,  limited  at  the  outer  end 
by  that  of  the  normal  cone,  as  shown  at  A.  But  this  is  open  to  the  objection,  which 
in  particular  cases  may  have  some  weight,  that  it  is  an  exact  representation  of  conical 
friction  gearing. 


PRACTICAL  HINTS  FOR  DRAUGHTSMEN. 


o" 
£ 


PRACTICAL  APPLICATIONS. 


EXAMPLE  XVII. 

32.  Drawing   of  a   worm   and   wheel.     Fig.    18. 

A  worm-wheel,  like  a  spur-wheel,  is  cut  out  of  the  solid  if  small,  and  if  larger  has 
arms  or  a  web  to  connect  the  rim  and  the  hub :  and  its  longitudinal  section  is  ac- 
cordingly drawn  in  a  similar  manner,  the  rim  being  always  cut  between  two  teeth  and 
the  hub  between  two  arms. 

But  in  making  the  section  of  the  rim,  we  have  here  a  new  state  of  affairs  owing 
to  the  twist  of  the  teeth :  a  plane  through  the  axis  would  cut  the  teeth  obliquely, 
making  a  very  confusing  representation.  Consequently  the  drawing  is  made  just  as 
though  the  rim  were  sawn  across  along  a  line  drawn  in  the  middle  of  the  space, 
making  a  twisting  cut. 

In  connection  with  this  section  of  the  wheel,  an  end  view  of  the  screw  is  given, 
the  correct  distance  between  the  centre  lines  being  laid  down  as  when  in  gear,  as 
shown  on  the  right  in  the  figure.  The  screw  is  not  shown  in  section  in  this  view, 
but  the  spindle  may  be  cut  off  in  front  of  the  screw,  as  shown  ;  the  engaging  tooth 
of  the  wheel  being  thus  concealed,  is  dotted  in. 

An  end  view  of  the  wheel  is  of  course  needed ;  but  in  a  working  drawing  this 
may  in  the  main  be  a  drawing  of  the  blank,  the  required  number  of  teeth  being 
marked  in  figures,  and  the  teeth  themselves  being  shown  only  so  far  as  to  include 
those  which  engage  with  the  screw,  and  one  or  two  more  on  each  side.  In  showing 
these  teeth,  the  preferable  method  is  to  make  a  section  of  the  rim  by  the  plane  xy, 
drawing  in  the  contours  of  the  teeth  as  thus  determined,  and  also  the  parts  of  them 
which  lie  beyond  the  plane  of  section :  these  last  should  be  true  projections,  but  if 
there  be  a  central  web.  it  should  not  be  shown  as  cut,  and  indeed  even  when  there 
are  arms,  it  is  as  well  to  show  the  inside  line  of  the  rim  in  full,  and  draw  the  arms 
as  though  they  were  beyond  the  cutting  plane. 

33.  The  side  view  of   the  screw  should    be    a    true    projection    and    accurately  drawn. 
This   will    of    course    hide    a    part    of    some    of    the    sectioned    teeth ;    and    in    order   to 
give    fuller  and    more  exact    information,  there   should    also   be   given,  as   at   A,  a  section 
of   the    screw,    in    which     the    pitch    line    of    the    rack    thus    formed     is    drawn,    and    the 
central    section    of    the    wheel  should    be    repeated,  drawing  it    as    in    gear  with    that  rack; 
with    an    arc    of   its    pitch    circle    also. 

The  above  suffices  for  a  shop  drawing  from  which  the  worm  gear  is  to  be  made. 
In  a  general  plan,  it  will  often  suffice  to  make  the  side  view  of  the  wheel  in  section ; 
but  hardly  so  with  the  end  view,  and  in  many  cases  it  is  necessary  to  show  both 
views  in  elevation. 

Then  there  is  nothing  for  it  but  to  face  the  guns  and  carry  the  battery:  as  in 
the  case  of  the  bevel  wheels,  a  drawing  in  projection  is  necessary  to  convey  any 
reasonably  good  idea,  if  the  scale  be  not  very  small :  though  as  no  measurements  are 
to  be  taken  from  it,  extreme  precision  in  constructing  the  curves  is  not  essential. 
On  a  very  small  scale,  it  may  be  admissible  to  make  a  mere  indication  by  drawing 


3o 


PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 


PRACTICAL  APPLICATIONS. 


t 


32  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 

the   pitch   cylinders   only,  with    lines   for   the  helical  teeth :    but  this  is   a   very  unsatisfac- 
tory  makeshift. 

EXAMPLE    XVIII. 

34.  A  connecting-rod,  with    one  "  pillow-block "   end ;    the   other   end   is   forked,   and 
each   arm   of   the   fork   terminates   in   a   "strap   and   end."     Fig.    19. 

This  drawing  illustrates  mainly  the  selection  and  arrangement  of  the  views  needed 
for  the  use  of  the  workman.  It  needs  no  reflection  to  perceive  that  a  top  view  of 
the  pillow-block  end  would  be  of  no  use  whatever;  all  the  information  not  contained 
in  the  front  view  is  conveyed  by  the  end  view  of  the  cap,  which  being  from  the 
left,  is  placed  at  the  left,  and  in  it  the  bolts  are  not  drawn,  their  whole  construction 
being  fully  explained  in  fact  by  the  drawing  of  the  upper  one  in  place,  in  the  front 
view :  still  the  detached  end  view  of  one  is  added,  as  it  adds  almost  nothing  to  the 
labor. 

In  regard  to  the  forked  end,  a  front  view  is  just  as  important  as  in  the  case 
of  the  pillow-block  end ;  but  here  an  end  view  would  be  very  obscure  and  of  no 
assistance  in  reading  the  drawing  or  in  making  the  rod,  which  absolutely  requires  a 
top  view.  The  peculiar  finish  of  the  fork,  however,  where  it  joins  the  round  shank, 
is  better  explained  by  a  section  through  ab,  looking  from  the  left  toward  the  right, 
which  is  accordingly  added. 

35.  Such   drawings   of   the   ends  of   connecting-rods   should    be   made  full  size,  or  on 
as   large   a   scale   as   convenient ;    but   it   is   not  at   all   necessary  to   place   the   centres  at 
the   full  distance   apart :    still,  a   drawing   of   the  shank   being   requisite,  of   its   full  length 
and    in    true    proportion,    this    is    made    on    a   smaller    scale    as    shown    above;    the    circles 
for   the    pins  are   drawn,  upon  whatever  scale    may  be    admissible,  at  the    correct    distance 
apart :    the    two    ends   of    the    shank   are    then    reduced    to    the    same    scale,    placed    in 
their   proper   relations   to   these   circles,   and    the   contour   of   the   shank   is   completed,  all 
the    paraphernalia    of   caps,  straps,  brasses,  etc.,  being    omitted.     If    the    shank    be    turned, 
as   is   very   commonly    the    case,    only   one    view    is    needed :    which    of   course    should    be 
drawn    upon   the   same   sheet    with    the   details   of   the   ends. 

EXAMPLE    XIX. 

36.  In    Fig.  20   is   shown   a   part   of   a   combination,   similar   to   the   "  Horton   Lathe 
Chuck,"   but   in   this   case   having   its   axis   vertical   when   set    up   in    place. 

This  casting  is  formed  with  ribs  on  the  upper  side,  and  facing  strips  on  the 
lower,  the  arrangement  of  which  cannot  be  clearly  shown  without  direct  views  of 
each  side. 

When  there  is  nothing  to  the  contrary,  it  is  no  doubt  a  good  idea  to  represent 
an  object  in  even  a  detail  drawing,  in  the  same  position  as  in  the  general  plan. 
Now  there  are  many  who  think  there  never  is  anything  to  prevent  this ;  and  in  such 
a  case  as  the  present,  it  is  not  unusual  to  find  the  piece  thus  shown :  a  view  from 
above  is  of  course  given,  and  easily  read  ;  —  but  there  will  also  be  given  a  "  view 
from  below,"  or,  as  it  is  frequently  labelled,  a  "  bottom  plan  ; "  which  is  not  easily 


PRACTICAL   APPLICATIONS. 


33 


34  PRACTICAL   HINTS  FOR    DRAUGHTSMEN. 

read,  for  the  simple  reason  that  it  is  seen  from  an  unusual  direction.  In  examining 
a  detached  piece  of  any  machine,  it  is  perfectly  natural  to  look  down  upon  it  from 
above,  especially  if  the  piece  has  a  horizontal  position  when  in  place :  but  nobody 
ever  gets  under  it  and  looks  upward,  in  order  to  ascertain  what  is  there,  if  he  can 
help  it.  This  ought  to  be  kept  in  mind  in  making  the  drawing;  the  draughtsman 
does  not  stand  on  his  own  head,  and  he  should  not  ask  other  people  to  stand  on 
theirs.  The  top  view  is,  naturally  and  correctly,  placed  over  the  side  view ;  and  the 
difficulty  is  sometimes  gotten  over  by  making  a  new  side  view  in  which  the  piece  is 
inverted,  and  drawing  another  top  view  over  that.  This  is  decidedly  better  than  to 
place  it  under  the  first  side  view  and  label  it  as  above  mentioned,  but  still  it  is  not 
always  very  easy  to  realize  the  correct  relations  between  the  upper  and  lower  parts 
when  drawings  are  thus  arranged. 

37.  The   advisable    expedient  is   to   place  the    piece    on  its    side   and  draw  it    in  that 
position ;    then    a  view  of  the    parts   on    the    left    placed  at    the    left,  and    a  view  of   those 
on    the    right    placed    at    the    right,  of    the    view    first    made,    will    be    readily    understood. 
Just    as   though    the    drawing    first    mentioned    were    the    south    front  of   a  house,  and  the 
other   two    the  west  and    east    fronts  respectively.     And  that    is  the    course  here  adopted : 
the   axis   is   placed    in    a   horizontal    position,  and  the   central  view  is   a   section    made    in 
accordance  with    the    principles    illustrated    in    Figs.  21    and    22. 

Over  this  is  placed  an  outside  view  of  a  small  portion  of  the  upper  part,  in  order 
to  define  clearly  the  semicircular  groove  in  the  outer  flange  on  the  left  side  of  the 
casting.  Above  the  view  at  the  left  is  given  so  much  of  a  section  by  the  plane  ab; 
looking  downward,  as  is  necessary  to  explain  the  relation  of  the  small  radial  ribs  thus 
cut,  to  the  surrounding  parts ;  and  this  also  shows  the  semicircular  groove  in  the  inner 
flange. 

This  groove  is  also  seen  in  the  section  at  A,  which  is  made  by  the  plane  cd, 
and  seen  from  the  direction  indicated  by  the  arrow.  It  may  be  said  that  this  section 
could  have  been  put  nearer  to  its  plane  by  drawing  it  on  the  other  side  of  the  large 
view — which  is  true ;  but  if  that  were  done  the  arrow  ought  to  be  reversed  and  the 
section  looked  at  in  the  opposite  direction,  which  would  not  be  so  clear  nor  so  ex- 
planatory. 

I 

EXAMPLE    XX. 

38.  Fig.    21    exhibits    the    Slide-valve,     Valve-chest,    Valve-seat    and    a    part    of    the 
Cylinder  of   a    horizontal    steam-engine. 

This  example  illustrates  the  advantage  of  selecting  cutting  planes  in  such  a  way  as 
to  show  clearly  what  is  desired ;  using  in  the  same  view  as  many  different  planes  as 
may  be  found  necessary  or  convenient. 

The  longitudinal  section  of  the  cylinder  and  valve-chest  is  by  the  plane  ab;  but 
that  of  the  valve  is  by  the  plane  cd,  which  evidently  shows  its  structure  more  clearly. 

In  the  top  view,  the  valve-chest  is  cut  by  a  horizontal  plane  through  the  centre 
of  the  valve-stem  and  steam-pipe.  But  the  valve  and  stem,  and  the  stuffing-box,  as 
well  as  the  bolts,  are  omitted.  The  bolts  pass  through  half-sleeves  cast  on  the  outside 


PRACTICAL   APPLICATIONS. 


35 


36  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 

of  the  wall  of   the  chest,  and  this  drawing  is  much  clearer   than  it  would   be  if  the  bolts 
were  shown   in   section. 

The  relation  of  the  chest  to  the  valve-seat  is  made  more  distinct  by  omitting  the 
valve  (of  which  a  detached  top  view  is  given  over  the  transverse  section),  and  showing 
the  seat  with  its  ports.  But  this  last  would  of  course  be  repeated  in  the  drawing  of 
the  cylinder,  (in  which  the  valve-chest  would  be  removed,)  exhibiting  the  hubs  which 
must  be  provided  for  the  standing  bolts  at  the  end  of  the  chest,  as  well  as  the  ex- 
haust opening.  These  last  items  are  therefore  omitted  in  this  drawing,  the  seat  alone 
being  all  that  is  needed  in  connection  with  the  valve  and  chest. 

39.  In    the    transverse    section,    the     cylinder    and    valve    are    cut   by    the    plane    wz 
through   the  centre  of   the    exhaust    port  and    pipe.     But    this   plane,  obviously,  would  cut 
the    valve-chest    in    a   very  unsatisfactory   manner,  for    it    passes    through    the   axes    of    the 
two    central    bolts.       Therefore,    the    plane  xy   through    the    centre    of    the    steam-pipe    is 
chosen  instead.     Nevertheless,  the  middle  bolt  on  the    right-hand  side  is  dotted  in  ;  for  it 
must    somehow    and    somewhere    be    shown    that    a    standing   bolt    must    be    used    in   this 
position  also  ;   and  it  can   be   shown  nowhere  else   so  well   as  here.     Nor  does  this  in  the 
least  confuse    the  drawing,  for  the  outline    of   this  bolt  coincides  exactly  with  that  of  one 
beyond  the    cutting  plane.       The    plane   xy,  in    the  present    instance,  passes  between    two 
bolts   on  the  left-hand    side  of   the    steam-chest,  which    is   therefore  shown    as   also  cut  by 
this    plane   in    the    transverse    section,  so    that  the  main  wall  of   the   chest  is  shown    in  its 
true   relation   to    its   flanges,    the    half-sleeve    surrounding   the   bolt   beyond   is.   shown    in 
outside  view,  and    the  bolt  itself  is  dotted   in. 

Thus  in  each  of  the  two  lower  sections,  two  different  cutting  planes  are  employed  ; 
and  had  a  bolt  chanced  to  lie  opposite  the  steam-pipe,  there  would  have  been  no  hes- 
itation in  cutting  the  left-hand  side  of  the  chest  by  a  third  transverse  plane  which 
should  not  pass  through  the  axis  of  that  bolt. 

The  advantage  in  respect  to  compactness,  by  adopting  the  methods  here  explained, 
is  self-evident,  as  all  the  sections  made  use  of  are  necessary.  Nor  is  there  a  point 
left  in  doubt,  with  the  single  exception  of  the  arrangement  of  the  interior  of  the 
stuffing-box ;  in  a  plan  on  a  practical  scale,  this  would  be  dotted  in,  and  made  distinct 
by  sectioning  over  the  outlines,  as  in  Figs.  27  and  28. 

40.  It    is  not    pretended    that    the    above    examples    include    all   the  infractions  of    the 
laws   of  projection,  or   departures    from    the  methods  of   descriptive    geometry,  which  may 
be    found    useful.       But    though    it    is    hoped    that    they    include    a    sufficient    number    to 
be    of   practical    service,  the  writer   still    more    strongly  desires    that    they  may   prove    sug- 
gestive   of   others,  and  that    the    reader,  freeing   himself    from    the    trammels    of   precedent 
and    prejudice,  may  make    rapid    progress  toward     the    highest    efficiency :    which    it    is   as 
vain    to    expect   of   the    rigid    formalist,  as    it  is  to    look    for   the   healthy  growth    and    full 
development   of   a   bark-bound   tree. 


ON   THE  REPRESENTATION  OF  BOLTS,   NUTS,   SCREWS,   AND  RIVETS.  37 


CHAPTER   II. 

ON  THE   REPRESENTATION   OF   BOLTS,   NUTS,   SCREWS,  AND   RIVETS. 

1.  In  every  working  drawing,  it  is  essential  that  the  fastenings,  such  as  bolts,  screws, 
and  rivets,  should  be  as  clearly  indicated  as  any  other  detail. 

But  it  does  not  follow  that  they  need  be  drawn  with  the  same  degree  of  precision.  For 
in  every  machine-shop  a  system  of  some  kind  is  adopted,  in  which  the  diameter  of  a  bolt 
determines  the  number  of  threads  per  inch,  as  well  as  the  sizes  of  the  head  and  the  nut.  So 
that  in  respect  to  these  particulars  it  does  not  matter  whether  the  drawing  be  made  in  exact 
accordance  with  the  standard  or  not ;  and  much  time  may  be  saved  by  adopting  the  following 
methods  of  representation : 

2.  Bolt-heads  and  nuts  are  usually  either  square  or  hexagonal ;  and  it  is  clearly  a  con- 
venience, in  making  the  wrenches,  to  have  the  side  of  the  square,  and  the  breadth  or  "  short 
diameter"  of  the  hexagon,  of  sizes  that  can  be  readily  set  off  by  the  scales  in  common  use. 
Consequently  in  the  case  of  the  hexagon,  the  "  long  diameter,"  or  distance  from  corner  to 
corner,  will  involve  an  awkward  decimal.     This  is  of  no  consequence  in  making  the  nut,  but 
would  be  very  inconvenient  in  making  the  drawing:  for  the  side  view  of  a  bolt  should  invari- 
ably be  such  that  there  is  no  possibility  of  doubt  or  error  as  to  the  shape  of  either  the  head  or 
the  nut ;  if  square  the  sJiort  diameter,  if  hexagonal  the  long  diameter,  should  be  parallel  to  the 
paper. 

3.  Calling  the  diameter  of  the  bolt  unity,  the  proportions  given  below  will  be  found  very 
convenient  in  practice,  being  simple  and  easily  remembered. 

Side  of  Square  Nut,     if;  Depth,  I. 

Head,  i*  ;       "        f . 

Long  Diam.  Hex.  Nut,    2;         "        I. 

"    Head,  i  J ;       "        |. 

It  is  only  in  very  massive  machinery  that  bolts  used  as  fastenings  are  over  i^-  inches  in 
diameter :  up  to  that  size,  the  proportions  just  given  do  not  differ  materially  from  the  stand- 
ards in  general  use,  and  the  saving  of  time  effected  by  employing  them  is  sufficient  in  many 
cases  to  be  of  very  considerable  importance.  Tables  for  the  U.  S.  and  the  Whitworth  Stand- 
ard systems  may  be  found  in  the  Appendix. 

4.  Through  Bolts. — Fig.  22  shows  two  pieces  of  metal  secured  together  by  what   is 
called  a  through  bolt,  with  hexagonal  head  and  nut. 

The  bearing  side  of  the  nut  has  its  corners  rounded  off,  since  otherwise  the  sharp  edges 
and  angles  would  scrape  and  catch  upon  any  inequalities  on  the  surface  against  which  it  bears, 
thus  possibly  preventing  the  bolt  from  binding :  for  a  contrary  reason  the  corners  of  the  head 
are  not  rounded  off  on  the  bearing  side,  though  on  the  other  side  they  may  be  as  a  matter  of 
taste  in  respect  to  appearance. 


38  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 

Now  as  to  the  manner  in  which  this  rounding  off  is  represented.  The  point  b  is  first 
located,  either  by  describing  about  c  an  arc  with  radius  cd,  or  drawing  with  the  60°  triangle  a 
line  through  c  at  an  angle  of  30°  with  the  centre  line  ;  then  a  horizontal  through  b  locates  the 
points  a,  e,  f:  by  trial  and  error  the  bow-pen  is  set  to  draw  an  arc  through  a  and  b,  tangent  to 
the  lower  side  of  the  nut,  and  with  this  radius  the  four  arcs  shown  are  drawn. 

Be  it  understood  that  this  process  does  not  represent  precisely  the  effect  of  turning  off 
the  end  of  the  nut  in  the  form  of  part  of  a  sphere,  which  will  be  discussed  farther  on.  But  it 
answers  perfectly  the  practical  end  in  view,  which  is  to  indicate  that  the  corners  are  by  some 
means  to  be  prevented  from  scraping. 

The  bolt  projects  very  slightly  above  the  top  of  the  nut.     This  is  shown  by  two  vertical 


•*- 1 


H-l 


-A- 


FIG.  22. 


FIG.  23. 


FIG.  24. 


lines,  just  long  enough  to  "  show  daylight  "  between  the  top  of  the  nut  and  the  horizontal  line 
mn,  no  attempt  being  made  to  represent  the  screw-thread :  and  finally  the  top  of  the  bolt  is 
finished  off  by  a  circular  arc  about  centre  d.  ^ 

5.  In  Fig.  23  we  have  a  through  bolt  with  square  head  and  nut:  the  corners  of  the  nut 
are  in  this  case  shown  as  rounded  off  by  two  arcs  about  centres  g  and  h,  with  a  radius  equal  to 
the  depth  of  the  nut. 

And  in  Fig.  24  is  shown  a  through  belt  with  a  nut  at  each  end,  which  is  sometimes  made 
necessary  by  an  obstacle  that  prevents  a  headed  bolt  of  the  requisite  length  from  being  put  in 
place. 

In  this  case  it  is  hardly  necessary  to  say  that  only  the  nut  which  is  ordinarily  to  be 
removed,  should  have  the  bearing  side  rounded  off,  the  other  one  being  reversed,  since  in 
unscrewing  the  upper  nut  it  is  rather  desirable  than  otherwise  that  the  lower  one  should 
not  turn. 


ON    THE  REPRESENTATION   OF  BOLTS,   NUTS,    SCREWS,    AND   RIVETS.  39 


6.  Tap-bolts. — The  tap-bolt,  Fig.  25,  is  a  bolt  with  a  solid  head  ;  it  passes  through  the 
upper  piece,  and  is  screwed  into  the  lower  one ;  the  whole  bolt  being  turned  by  the  wrench 
applied  to  the  head,  of  which  the  corners  are  therefore  rounded  off  on  the  bearing  side. 

It  is  necessary  here  to  indicate  the  thread,  which  is  done  by  simply  drawing  the  "Vs"  as 
in  making  a  section  of  the  screw.  This  is  executed  by  first  drawing  lightly,  in  pencil  only,  two 
guiding  lines  on  each  side,  for  the  tops  and  bottoms  of  the  threads,  making  the  depth  of  the 
thread  about  \  the  diameter  of  the  bolt ;  after  which  the  sloping  lines  are  to  be  drawn  at  once 
in  ink,  using  a  common  steel  writing-pen  with  a  fine  point.  The  Vs  need  not  be  measured, 
but  are  to  be  drawn  free-hand,  making  a  light  up-stroke  and  a  heavy  down-stroke  to  represent 
a  shadow-line  on  the  section  thus  indicated  ;  but  it  is  not  material  which  side  of  the  V  is 
made  heavy.  This  work  should  be  done  as  regularly  and  evenly  as  possible,  the  angle  of  the 
Vs  as  nearly  60°  as  may  be  ;  and  in  order  to  avoid  the  natural  tendency  to  round  the  angles, 
care  must  be  taken  to  lift  the  pen  entirely  off  the  paper  at  the  end  of  each  stroke. 

The  thread  must  extend  above  the  face  rs,  to  a  distance  of,  say,  \  the  diameter  of  the 


n 


..J 


FIG.  25. 


FIG.  26. 


bolt,  and  attention  is  called  to  this  circumstance  by  a  dotted  line  op :  and  the  lower  end  of 
the  bolt  is  finished  by  a  transverse  line  and  a  circular  arc  of  radius  equal  to  the  diameter. 

7.  Standing  Bolts. — A  standing  bolt,  or  *  stud  "  as    it    is'   sometimes    called,  is  firmly 
screwed  into  one  of  the  two  pieces  to  be  connected,  and  remains  permanently  fixed ;  the  other 
piece  being  held  down  by  a  nut  on  the  upper  end  of  the  bolt,  as  in  Fig.  26.     The  thread  on 
the  lower  end  is  indicated  exactly  as  in  the  case  of  the  tap-bolt,  with  this  important  exception, 
viz.,  that  this  thread   of  the  standing  boll:*  must  terminate  exactly  at  the  face  of  the  lower 
piece. 

This  is  because  it  is  never  intended  to  come  out,  and  it  is  therefore  screwed  in  so  as  to 
make  the  thread  "  bottom"  or  "  jam,"  thus  fixing  it  so  firmly  that  it  will  not  work  loose  when 
the  nut  is  put  on  or  taken  off ;  and  the  length  of  this  lower  thread  should  when  practicable 
be  made  equal  to  i£  diameters. 

8.  Key-bolts. — In  circumstances  which  make  it  undesirable  to  use  either  of  the  fasten- 
ings above  described,  the  key-bolt,  Fig.  27,  is  sometimes  employed. 


40 


PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 


The  thickness  of  the  key  should  be  \  the  diameter  of  the  bolt,  its  breadth  \\  diameters, 
and  the  bolt  should  extend  beyond  the  key  to  a  distance  equal  to  f  the  diameter.  The  slot 
should  of  course  be  a  trifle  larger  than  the  key  in  each  direction  ;  that  is  to  say,  "an  easy  fit  " 
only  is  required ;  but  it  is  unnecessary  to  indicate  this  by  double  lines  in  the  drawing :  and  it 
makes  the  construction  much  more  distinct  to  show  the  key  in  section,  as  in  the  figure. 

The  above  remarks  relate,  be  it  noted,  only  to  the  representation  of  fastenings  in 
place,  that  is,  in  connection  with  the  pieces  which  they  hold  together :  and  it  is  proper  to  call 


FIG.  27. 


FIG.  28. 


attention  here  to  one  or  two  points  in  reference  to  the  preceding  illustrations,  and  some  of 
those  which  follow. 

1.  The  holes  not  tapped,  through  which  a  bolt  passes,  are  drilled  or  cored  a  little  larger 
than  the  bolt.     But  it  is  not  necessary  in  a  connected  plan  to  indicate  this,  (with  an  exception 
to  be  explained  presently,)  since  the  double  lines  would  confuse  the  drawing,  without  any 
advantage.     The  outline  of  the  bolt  is  drawn,  and  its  diameter  in  all  cases  marked  in  figures ; 
it  is  then  the  part  of  the  machinist  to  make  the  hole  for  a  bolt  of  that  size. 

2.  The  holes  which  are  tapped  must  of  course  be  made  a  little  deeper  than  the  length  of 
the  entering  part  of  the  bolt.     But  again,  confusion  would  arise  from  showing  this,  and  the 
drawing  of  the  bolt  being  made,  it  is  the  mechanic's  duty  to  make  the  hole  deep  enough  for  it. 


ON  THE  REPRESENTATION  OF  BOLTS,   NUTS,    SCREWS,   AND   RIVETS.  41 


If  separate  drawings  are  made  of  the  parts  to  be  bolted  together,  the  holes  are  there  to  be 
laid  out  of  the  size  and  depth  actually  required. 

3.  In  order  that  a  nut  may  "  draw  "  or  "  bind,"  the  bolt  must  be  threaded  for  a  distance  a 
little  greater  than  the  depth  of  the  nut. 

This  being  perfectly  well  understood,  and  implied  by  the  very  existence  of  the  nut,  the 
thread  need  not  be  indicated  in  a  connected  plan.  If  detail  drawings  of  the  bolts  are  made, 
the  thread  must  there  be  shown,  in  a  manner  which  will  be  illustrated  farther  on. 

10.  The  exceptional  case  alluded  to   in  the  preceding  section  is  illustrated  in  Fig.  28. 
The  bolt  being  of  considerable  length,  the  hole  is  "  chambered  "  for  some  distance  to  a  diam- 
eter much  greater  than  that  of  the  bolt.     This  chambering  is  therefore  shown  in  the  draw- 
ing— as  is  also  the  "  pocket  "  or  recess  formed  when  occasion   requires  for  burying  the  head  of 
the  bolt.     In  order  to  secure  alignment  the  upper  part  of  the  bolt-hole  is  often  reamed  so  as 
just  to  permit  the  bolt  (which,  however,  need  not  be  turned)  to  pass  through :  this  must  be 
noted  on  the  drawing,  as  in  the  figure. 

11.  The  reader  must  not  be  surprised  if  he  is  solemnly  assured  by  many  that  the  hex- 


J 


nn 


V-- 


FIG.  29. 


FIG.  30. 


FIG.  31. 


agonal  nuts  and  heads  herein  shown  are  all  wrong  side  up,  and  that  in  machinery  making  any 
pretension  to  finish,  the  corners  of  the  top  instead  of  the  bottom  should  be  rounded  off.  Also 
that  the  method  above  described  of  preventing  the  lower  corners  from  scraping  is  not  the 
right  method,  but  that  this  object  ought  to  be  accomplished  by  turning  the  lower  side  so  as  to 
form  a  very  thin  cylindrical  collar  of  a  diameter  equal  to  the  inscribed  circle  of  the  hexagon. 
This  is  merely  a  matter  of  taste  :  and  neither  style  has  any  practical  advantage  over  the  other. 

12.  Screw-driver  Heads. — Bolts  with  round  heads,  slotted  for  the  application  of  a 
screw-driver,  are  rarely  used  in  heavy  work,  but  those  of  small  size,  called  "  machine  screws," 
are  extensively  employed  in  lighter  constructions.  Even  in  that  case,  they  should  be  correctly 
represented ;  and  they  are  occasionally  met  with  up  to  \\  inches  in  diameter  ;  most  fre- 
quently when  the  head  must  be  countersunk. 

Suitable  proportions  are  shown  in  Fig.  29;  calling  the  diameter  of  the  bolt  I,  as  usual 
that  of  the  cylindrical  head  is  if,  its  depth  |,  the  slot  being  \  wide  and  £  deep. 


PRACTICAL    HINTS   FOR    DRAUGHTSMEN. 


By  rounding  off  the  top  corners  with  a  radius  of  ^,  as  in  Fig.  30,  we  have  the  "  fillister- 
headed  "  machine  screw,  the  smaller  sizes  of  which  are  largely  used  in  model  work  and  light 
mechanism  of  a  similar  kind.  The  heads  of  these  small  screws  are  also  sometimes  made  of  a 
hemispherical  form.  But  if  made  exactly  so,  the  effect  is  unpleasing,  and  a  preferable  contour 
is  given  in  Fig.  31.  The  diameter  of  the  head  is  if,  and  the  sides  da,  eb,  are  vertical  for  a 
distance  of  \.  From  centres  c  *-on  ab  two  circular  arcs  are  drawn  with  a  radius  of  £,  and  these 
are  joined  by  an  arc  about  a  centre  o  on  the  centre  line,  lying  -^  below  the  bottom  of  the  head  : 
the  slot  is  £  wide  and  f  deep. 

13.  By  counterboring  the  piece  against  which  it  bears,  the  cylindrical  head  shown  in  Fig. 
29  may  be  partially  buried — or  even  entirely  if  that  piece  be  thick  enough.  If  it  be  not  thick 
enough,  and  it  be  desirable  nevertheless  to  make  "  flush  work,"  the  conical  head,  Fig.  32,  is 


-" 


— "f- 


«OK>> 


1 

I 


-__£. » 


FIG.  32. 


FIG.  33. 


FIG.  34. 


used.  The  larger  diameter  is  2,  depth  of  frustum  £,  slot  £  wide  and  f  deep.  If  not  required 
to  be  absolutely  flush,  the  depth  of  the  frustum  may  be  made  £,  as  in  Fig.  33,  and  the  top  of 
the  head  finished  off  with  a  circular  arc  having  a  radius  of  2^,  the  size  of  the  slot  remaining 
unchanged. 

14.  Wood-screws. — The  angle  of  the  Vs,  in  representing  the  wood-screw,  Fig.  34,  should 
be  less  than  60°,  say  about  45°,  and  the  threads  separated  by  a  small  distance  at  the  bottom. 
The  "  gimlet  point  "  is  indicated  by  finishing  the  end  of  the  screw  with  two  concave  arcs  as 
shown  ;  the  slope  of  the  conical  head  is  45°,  the  depth  T9T  of  the  diameter  of  the   screw  ;    the 
slot  £  wide  and  f  deep.     These  dimensions  are  larger  than  those  found  in  many  of  the  screws 
in  market,  a  very  common  defect  in  which  is  a  slot  too  small  to  give  sufficient  bearing  surface, 
the  result  being  that  the  edges  yield  and  the  slot  quickly  becomes  useless;  a  most  vexatious 
experience  familiar  to  all. 

15.  Detail  Drawings  of  Screws. — In  many  machine-shops  it  is  customary  to  make,  for 
any  engine  or  machine  in  hand,  a  "  bolt  sheet,"  showing  all   the  different  kinds  and  sizes  ot 
bolts,  nuts,  screws,  etc.,  required,  with  the  number  of  each. 


ON    THE  REPRESENTATION  OF  BOLTS,   NUTS,    SCREWS,    AND  RIVETS.  43 

A  good  practical  method  of  indicating  the  screw-thread  is  shown  in  Fig.  35  ;  the  exterior 
outline  of  the  bolt  being  drawn  in  ink,  the  guiding  lines  for  the  bottoms  of  the  threads  are 
lightly  pencilled;  but  instead  of  drawing  the  Vs,  the  threads  are  indicated  by  a  series  of  par- 
allel lines,  alternately  long  and  short,  properly  inclined  as  required  by  the  pitch.  The  inclina- 
tion is  very  readily  determined  as  shown  at  the  right  of  the  figure ;  the  section  ebc  of  a  single 
thread  being  drawn  with  the  60°  triangle,  then  since  the  root  on  one  side  of  the  bolt  is  opposite 
the  crest  on  the  other,  ca  is  drawn  "  square  across,"  and  ab  is  the  desired  slope.  Setting  the 
triangle  by  this  line,  then,  the  parallels  are  drawn  at  once  in  ink,  the  spacing  being  done  by  the 
eye,  as  in  sectioning.  Since  the  crests  of  the  threads  cast  shadows,  the  long  lines  should  be 
made  heavy ;  which  is  best  done  by  going  again  over  each  with  the  pen,  as  soon  as  it  is 
drawn. 

16.  This  is  a  purely  conventional  way  of  indicating  a  screw-thread ;  it  is  not,  and 
does  not  pretend  to  be,  a  drawing  of  it  in  any  proper  sense ;  but  it  answers  the  pur- 
pose in  view  just  as  well  as  the  most  accurate  representation. 

Moreover,  at  a  little  distance  a  drawing  of  a  small  screw  thus  made  actually  looks 
like  a  screw,  whether  it  is  like  it  or  not — much  more  so  than  it  would  be  likely  to  were 


FIG.  35. 


the  Vs  drawn  with  the  triangle,  especially  if  the  pitch  be  fine ;  in  which  case  the  most 
painful  accuracy  in  the  use  of  the  instruments  is  necessary  to  avoid  variations  in  the 
diameter,  which  are  always  conspicuous  even  if  small,  and  utterly  ruinous  to  the  effect: 
whereas  trifling  errors  in  the  spacing  of  the  parallel  lines  do  not  force  themselves  upon 
the  attention  to  anything  like  the  same  extent. 

17.  If  the  bolt  is  very  large,  the  above  modes  of  representing  it  in  full-size 
drawings  are  not  eligible.  It  is,  however,  very  rarely  that  one  is  used  of  such  dimensions 
as  to  make  it  worth  while  to  construct  an  exact  projection  of  it,  introducing  all  the 
details  of  the  flattening  of  the  crest  at  the  top  and  the  groove  at  the  bottom,  the  helical 
curves  of  the  thread,  etc.  As  a  compromise  between  this  and  the  preceding  processes, 
that  shown  in  Fig.  36  may  be  used  with  good  effect. 

This  consists  in  laying  out  the  section  of  a  "  full  sharp"  V-threaded  screw,  which  is 
carefully  inked  in  with  the  aid  of  the  60°  triangle,  after  which  the  tops  of  the  threads 
are  joined  by  one  series  of  parallels  (made  heavy,  as  being  shadow-lines\  and  the  bot- 
toms by  another  series,  which  of  course  have  a  slightly  different  inclination. 

It  is,  certainly,  possible  that  a  bolt  may  be  required,  in  very  massive  machinery,  so 
large  that  it  may  be  desirable  to  show  the  outline  in  this  manner  even  in  a  plan  where 


44  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 

the  bolt  is  drawn  "  in  place."  But  this  should  not  be  done  if  the  pitch  be  much  if  any 
less  than  half  an  inch,  or  the  effect  will  be  merely  that  of  a  mass  of  dots  ;  and  far  less 
distinct,  while  much  more  laborious,  than  that  of  the  method  first  described. 

18.  Exact  Drawing  of  a  Nut. — On  the  other  hand,  if  the  nut  be  very  large,  it  may 
be  worth  while  to  represent  precisely  the  effect  of  turning  it  off  to  a  spherical  form  at 
the  end. 

Let  the  axis  of  the  hexagonal  prism,  and  the  dotted  great  circle  of  the  sphere  whose 
centre  is  c  in  Fig.  37,  lie  in  the  plane  of  the  paper,  LL  representing  a  plane  perpendicular 
to  the  axis,  Then  all  the  edges  of  the  prism  pierce  the  sphere  at  the  same  distance 


FIG.  36. 


FIG.  37. 


from  LL,  to  which  therefore  abdc  will  be  parallel.  The  front  face  of  the  prism  cuts 
from  the  sphere  a  small  circle,  of  which  the  arc  bid,  whose  centre  is  c,  will  be  visible, 
and  since  this  face  is  parallel  to  the  paper,  this  arc  will  be  seen  in  its  true  form. 

Equal  circles  will  be  cut  from  the  sphere  by  the  other  visible  faces ;  but  since  these 
faces  are  inclined  to  the  paper,  the  arcs  akb,  dme,  will,  strictly,  appear  as  parts  of 
ellipses,  the  middle  points  k,  m,  of  these  arcs  being  the  extremities  of  the  major  axes. 
The  distance  of  these  points  from  LL  will  of  course  be  equal  to  cl;  therefore  if  the 
nut  be  finished,  as  is  usual,  by  a  transverse  plane  through  /,  it  will  suffice  in  practice  to 
draw  through  that  point  the  horizontal  line  in,  and  to  draw  akb  as  a  circular  arc  tan- 


ON   THE  REPRESENTATION  OF  BOLTS,   NUTS,    SCREWS,    AND   RIVETS.  45 


gent  to  in;  finding  the  centre  by  trial  and  error.  Thus  it  is  seen  that  the  short-hand 
representation  adopted  in  the  working  drawing  differs  from  this  exact  construction  only 
in  the  omission  of  the  portions  aik,  enm,  and  the  substitution  of  two  arcs  of  a 
shorter  radius  for  the  flatter  arc  bid:  but  these  apparent  trifles  will  be  found  to  effect 
a  material  saving  of  time  and  trouble  where  many  nuts  of  the  same  size  are  to  be 
drawn. 

19.  Rivets. — By  the  use  of  the  hand-hammer,  the  form  given  to  the  outer  head  of 
a  rivet  is  approximately  conical ;  and  it  may  be  represented  in  either  of  the  two  ways 
shown  in  Fig.  38,  the  diameter  of  the  base  of  the  cone  being,  in  each,  twice  that  of  the 
rivet,  which  is  taken  as  unity. 

The  one  on  the  left  is  more  readily  drawn,  the  head  being  an  exact  cone  whose 
altitude  is  f.  The  one  on  the  right  is  a  stronger  form,  bounded  by  two  circular  arcs, 
each  struck  with  a  radius  of  if  about  a  centre  on  the  opposite  side  of  the  outline  of 
the  body  of  the  rivet;  thus,  the  arc  ab  is  described  about  c  as  a  centre.  The  lower,  or 


«.--  --a 


tlM 
.  ..* 


V 


7 


FIG.  38. 

original,  head  of  the  rivet  is  in  the  form  of  a  truncated  cone,  the  larger   diameter   being 
if,  the  smaller  diameter  ij,  and  the  depth  f. 

20.  If   a   die   (sometimes  called  a  "snap"   or  a   "button-set")   is   used    instead   of    the 
hand-hammer,  the  "cup-head"  thus  formed  may  be  represented   as   shown    on  the  left  in 
Fig.  39.     This  is  not  a  complete  hemisphere,  its  diameter  on  the  flat    face  being    if,  and 
the  centre  of  the  curve   being  £  below  the   face. 

In  machine-riveting  the  finish  may  be  the  same  at  both  ends,  as  shown  on  the  right 
in  the  same  figure ;  and  of  course  a  round-headed  rivet  may  be  riveted  over  with  the  hand- 
hammer  if  desired. 

21.  Countersunk  Rivets   may   be    made  "  dead    flush,"  as   shown    in    the  left  in    Fig. 
40, 'or  finished  with  a  slightly  convey   surface,  as   shown    on   the  right;    the   latter   being 
preferable  when  circumstances  admit.     In  either  case,  the  depth  of  the  countersink   is  £, 
its  larger  diameter   if;   and   the    second  one  has,  in  addition  to  the  cone  thus  formed,  a 
projecting  spherical  swell  of  which  the  radius  is  2\. 


46 


PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 


22.  It  is  to  be  kept  in  mind,  that  this  chapter  relates  to  the  representation  and 
indication  of  things  in  the  execution  of  which  it  is  not  essential,  nor  expected,  that  the 
mechanic  shall  be  governed  by  the  precise  dimensions  of  the  drawing.  And  in  like  man- 
ner, it  is  not  essential  that  in  adopting  the  proportions  herein  suggested,  the  draughts- 


V 


7 


FIG.  39. 

man  should  be  over-scrupuious  in  carrying  them  out  with  minute  accuracy ;  common- 
sense  should  be  exercised  in  respect  to  rejecting  such  insignificant  fractions  as  would  in 
some  cases  result  from  a  rigid  adherence  to  them.  Indeed,  it  is  not  advised  to  make 
computations  at  all  in  these  matters:  the  diameter  of  the  bolt  or  rivet  being  accurately 


f  1 


f 


FIG.  40. 

set  out,  the  fractions  of  that  magnitude  used  in  laying  out  the  other  parts  can,  with  a 
very  little  practice,  be  at  once  taken  up  with  the  compasses,  by  the  eye,  with  all  the 
precision  needed  for  the  purpose  of  making  working  plans. 


ON  FREE-HAND  SKETCHING.  47 


CHAPTER  III. 
ON  FREE-HAND   SKETCHING. 

Sketching  in  Proportion. — Its  Utility  in  Designing. — Sketching  from  Measurement. — Methods  of 

Practising.— Practical  Suggestions  and  Examples. 

1.  It  is  supposed   by   some,  that  deft  handling   of  instruments   of  precision  alone  is 
required  of  the  mechanical  draughtsman.     This,  however,  is  an  error;  no  matter  how  expert 
he  may   be  in   the  execution  of   working   plans  by   rule  and  compass,  the  measure   of  his 
accomplishments  is  not  yet  full  if  he  lack  the  ability  to  make  good  free-hand  sketches. 

To  the  designer  of  a  new  machine  of  any  degree  of  complexity,  a  fair  degree  of  skill 
in  this  direction  is  absolutely  essential.  He  may  have  the  clearest  possible  conception 
of  the  relations  of  the  parts  and  of  the  general  arrangement  of  the  whole,  but  without 
some  visible  record  of  that  conception,  to  which  reference  can  be  made  from  time  to  time 
he  cannot  proceed  with  any  certainty  of  success  in  the  elaboration  of  the  details.  This 
record  is  in  the  nature  of  a  sketch,  though  not  necessarily  wholly  free-hand  Sometimes 
certain  absolute  dimensions  are  assigned  as  a  basis,  such  for  example  as  the  bore  and  the 
stroke  in  a  steam-engine. 

Or  again,  definite  movements  must  be  provided  for,  and  their  elements  reduced  to 
settled  proportions,  as  a  preliminary ;  the  resulting  diagram  forming  the  skeleton  of  the 
proposed  structure.  In  either  case  some  use  of  scale  and  instruments  is  of  course  proper, 
not  to  say  necessary;  but  the  filling  out  of  this  skeleton  into  the  complete  body  is 
largely  dependent  upon  free-hand  work. 

2.  Usually  this  dependence   is   direct,  the   designer  at   once   sketching   in  the   general 
arrangement,  for  the  sake  of  having  something  before  him  as  a  guide  in  subsequent  opera- 
tions ;    and  his  sketch-plan   serves   him   as  the   clay  serves   the   sculptor,   being   subject   to 
erasures  and  alterations  as  the  development  of  his  scheme  may  suggest  or  demand. 

In  simple  cases,  however,  he  may  proceed,  without  this,  to  construct  the  details,  adding 
them  successively  to  his  skeleton  drawing,  as  each  is  completed.  But  whether  this  be 
done  or  not,  these  details  are  but  the  individual  figures  in  the  group,  and  each  can  be 
finished  with  greater  ease  and  certainty  in  the  marble  if  first  modelled  in  the  clay.  In 
designing  them,  the  problems  are  less  comprehensive,  but  their  nature  is  the  same;  the 
skeleton  plan  indicates  certain  pins,  which  must  be  connected  by  a  link;  it  locates  certain 
journals,  and  these  must  be  supported  by  a  frame  with  suitable  bearings;  it  gives  the 
positions  of  certain  orifices,  which  are  to  be  joined  by  pipes  with  valves ;  and  so  on  in 
endless  variety  of  condition  and  requirement.  One  of  these  problems  seldom  admits  of 
a  single  absolute  solution,  which  must  be  accepted  to  the  exclusion  of  all  others.  Some- 
times tentative  methods  are  necessarily  adopted :  and  in  most  cases  there  is  a  choice  of 
ways  and  means,  so  that  a  judicious  selection  can  be  made  only  by  comparison :  in  either 
event  the  utility  of  reasonably  accurate  sketches  is  self-evident,  and  from  the  nature  of 


48  PRACTICAL  HINTS  FOR  DRAUGHTSMEN. 

things  it  is  equally  apparent  that  they  can  be  made  most  advantageously  with  the  free 
hand,  whether  for  the  use  of  the  maker  only,  or  for  submission  to  the  inspection  and 
decision  of  another. 

3.  But   before   attaining  to  the   position   of   a   designer,   the  draughtsman  will   in   the 
usual  course  of  events  be  confronted  with  circumstances  in  which  such  sketching  is  indis- 
pensable.     Machines   will  break  down ;    and   it  is   very  frequently  necessary  to   replace  a 
broken   piece   in   the  absence   of   the  drawing  from  which    it   was  made.       Or   a   drawing 
may  be  lost  after  a  piece  is  finished,  and  a  new  one  is  required.     If  the  part  in  question 
be  small   and    portable,    it   might   be   brought   into   the    drawing-office,    and   the   measure- 
ments as  taken  off   be  set  out  at  once   by  scale ;    but  in  general   this  is  not  practicable, 
and  a  sketch  must  be  made  and  the  object  measured  wherever  it  may  happen  to  be. 

Again,  in  the  case  of  machines  already  built,  additions  or  alterations,  often  called 
for,  require  accurate  definition  of  all  surroundings,  in  order  that  the  new  parts  may  go 
properly  into  place  and  action,  without  interfering  with  the  old  ones ;  and  such  changes 
must  frequently  be  made  elsewhere  than  in  the  original  constructing  shop,  so  that  the 
working  drawings  are  inaccessible.  It  devolves  upon  the  draughtsman  to  obtain  the 
requisite  data  as  a  basis  of  operations,  and  his  first  services  are  to  be  rendered,  not  with 
his  drawing  apparatus,  but  with  the  mechanic's  callipers,  squares  and  rules,  wherewith 
he  makes  the  measurements  to  be  noted  on  a  free-hand  sketch.  And  he  who  can  do 
this  well, — who  can  be  relied  on  to  make  no  oversights  or  mistakes,  but  to  return  to  the 
office  with  a  clear,  distinct,  and  accurately  figured  sketch,  so  that  the  work  may  be  pro- 
ceeded with  in  perfect  confidence,  is  the  fortunate  possessor  of  a  most  valuable  qualifi- 
cation. 

4.  It  is  advantageous  if  there  be  much  of  this  kind  of   practice,  for  it  is  of   threefold 
utility.      Not  only  are  the  sketches    directly  made   use   of    for   their  special  purposes,  but 
in  the  very  process  of  making  them  and  the  necessary  measurements,   the  habit   of   close 
observation  is  cultivated,,  and,  in  addition,  impressions  of  relative  if  not  of  absolute  dimen- 
sions insensibly  fix  themselves  in  the  mind,  and  what  may  be  called  a  sense  of  proportion 
is  developed,  which  to  the  designer  is  of  the  greatest  value.      For  in  planning,  it  is  per- 
fectly  clear   that  those  sketches  are  the    best    which   most    closely  resemble    the    drawings 
when  finally  worked  out,  since   the  latter  must  embody  the   results  of  calculations  based 
upon  the  known  properties  of  materials  and  the   conditions  that  must    be  fulfilled.      And 
in  making  them,  the  free  hand  is  guided  in   unconscious   conformity  with  the    results   of 
experience  and  with    unwritten  deductions  from  successful   practice,  just   as  the   style  of  a 
writer  is  influenced  without    his   knowledge   by  the  books  he  has  read  ;  and  the  more  ex- 
tensive and  varied   the   store  of  precedents,  the  better  is  it  likely  to  be  guided.     And  be 
it  understood,  that    this  acquisition  does  not  make  the  designer  a  copyist,  any  more  than 
a  wide   range   of  reading  makes  a  plagiarist  of   an  author;  but   the  one  is  more  likely  to 
put  his  original  conceptions    into  good    practical   forms,  and   the  other  to  put  his  original 
thoughts  into  terse  and  telling  words. 

5.  In  "sketching  from  measurement,"  the   dimensions   are   always   given   in  figures; 
so  that  the  scale  drawing  must  be  like  the  object,  whether  the  sketch  is  or  not.     Whence 
some  make  the  inference,  and  what  is  worse  they  act  upon  it  too,  that  care  with  the  lines 
is  useless  if  only  the  figures  are  right ;  and   are  content  with  records  so  rude  that  no  one 


ON  FREE-HAND   SKETCHING,  49 

else  can  read  them,  and  they  themselves  cannot  do  it  after  a  short  time  has  elapsed. 
They  tacitly  assume  that  he  who  makes  the  sketch  is  also  to  make  the  scale  drawing. 
and  to  do  it  immediately ;  neither  of  which  is  by  any  means  always  the  case, — and  even 
if  it  were,  this  course  is  simply  throwing  away  an  opportunity  of  improvement. 

It  is  not  the  intention  that  any  reader  hereof  shall  make  so  gross  an  error.  Nothing 
but  the  most  extreme  urgency  can  excuse  such  slovenly  work,  and  in  all  ordinary  cases 
there  is  time  to  do  it  at  least  fairly  well.  A  good  sketch  is  a  permanent  record,  and 
either  the  maker  or  any  one  else  should  be  able  to  work  from  it  at  any  time :  and  no 
draughtsman  who  desires  to  improve  will  permit  himself  to  make  one  which  will  not 
pass  this  test. 

6.  The  power  to  sketch  new  details  in  good  mechanical  proportion,  previously  mentioned 
as  so  valuable  to  the  designer,  may  be  greatly  increased  by  practice.     And  the  following 
naturally  suggest  themselves  as  lines  in  which  such  practice  may  be  followed  to  advantage. 

1 .  Making  free-hand  copies  of  working  drawings. 

The  benefit  of  this  is  evident  from  the  fact  already  stated,  that  the  object  in  planning  is 
to  make  sketches  which  shall  serve  as  guides  in  making  the  scale  drawings.  It  need  hardly  be 
said  that  in  thus  copying,  the  proportions  should  be  preserved  as  closely  as  possible,  but  the 
scale  may  be  advantageously  varied. 

2.  Making  sketches  from  memory. 

This  will  be  found  a  most  beneficial  exercise,  either  for  the  student  or  the  professional 
draughtsman.  The  former  may  take  any  good  detail  drawing,  and  after  careful  examination 
and  study  of  its  various  parts  and  their  dimensions,  subsequently  make  sketches  as  nearly  in 
correct  proportion  as  he  can,  without  reference  to  the  original.  The  latter  may  do  the  same 
in  relation  to  any  plans  upon  which  he  may  be  engaged  during  the  day.  The  dimensions 
should  be  written  in  and  verified  by  subsequent  comparison  with  the  original. 

3.  Sketching  from  the  object  ivtt/iout  measuring. 

This  affords  the  best  of  training  for  both  eye  and  hand.  It  is  to  be  understood  that 
working  sketches,  not  perspective  representations,  are  to  be  made.  If  the  object,  which  may 
be  any  detail  of  machinery  that  happens  to  be  accessible,  is  small,  it  is  excellent  practice  to 
make  the  sketch  as  nearly  of  the  exact  size  as  possible  :  and  after  it  is  completed,  to  go  over 
it  with  a  scale  and  see  how  close  the  approximation  is.  If  the  piece  be  large,  the  sketch 
should  be  reduced,  and  subsequently  tested  in  a  similar  manner;  in  doing  this,  the  scale  of 
reduction  is  determined  by  comparing  the  magnitude  of  some  leading  part  in  the  sketch,  as 
for  instance  the  diameter  of  a  journal,  with  its  actual  size :  other  parts  ought  of  course  to  be 
found  reduced  in  the  same  ratio. 

7.  This  last  must  not  be  confounded  with  the  ordinary  operation  of  "  sketching  from 
measurement,"  previously  spoken  of,  although  in  some  respects  similar.     It  is  to  be  regarded 
as  an  exercise  pure  and  simple,  and  its  object  would  be  defeated  were  the  measurements  taken 
beforehand ;    nor    is    rapidity,   at   least  in  the   beginning,  a   special   desideratum,  although 
ultimately  it  is  a  point  of  some  consequence.     Whereas  in  the  other  case  time  is  usually  an 
important  item,  and  a  material  saving  in  this  respect  may  often  be  made  by  taking  some  of 
the  leading  dimensions  before  beginning  the  sketch ;   besides,  the  main   object  here  is  to 
obtain  a  record  of    the  measurements,  which  must  be  figured  in,   clearly  and   without   the 
possibility  of  erroneous  interpretation.     This  is  absolutely  indispensable ;  if  it  can  be  done. 


5o  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 

and  the  sketch  still  have  all  parts  in  correct  proportion,  so  much  the  better.  But  this  is  not 
always  the  case,  and,  as  will  be  explained  presently,  advantages  may  often  be  gained  by 
purposely  sketching  out  of  proportion,  which  also  the  draughtsman  should  know  how  and 
when  to  do.  Such  liberties,  it  is  needless  to  say,  are  wholly  out  of  the  question  in  the 
practice  of  the  preceding  exercise. 

PRACTICAL  SUGGESTIONS. 

8.  It  will  have  been  gathered  from  the  foregoing,  that  in  general  a  good  sketch  is  equiva- 
lent to  a  working  drawing  made  with  the  free  hand  instead  of  by  the  aid  of  instruments:  with 
the  one  as  with  the  other,  the  object  is  to  show  what  to  do  and  how  to  do  it,  and  neither 
is   perfect    if   in    any  particular   there    is   a    deficiency  or  a  doubt.     But    experience  proves 
that   one   may  be   quite  competent  to   make  a  drawing   of   any  mechanical   detail  from  a 
figured  sketch,  and   yet  fail   to  produce  a  satisfactory  sketch  if  the  piece  itself  be  placed 
before  him.     Just  as  with  everything  else,  practice   is   necessary  in   order  to  do  this  with 
facility ;  written  instructions  could   hardly  be   made  to   cover   every  contingency,  but  still 
some  hints  may  be    useful    to   the  novice,  and    enable  him    to  avoid   many  errors   unfortu- 
nately  too   common.      The    causes   of    such    failures   are   various ;    but    one   of   the   most 
prominent  is  a  misconception  of  what  is  wanted. 

Beginners  are  very  apt  to  think  that  an  exact  duplicate  is  to  be  made  of  what  they 
are  required  to  sketch,  and  to  expend  much  labor  in  measuring  minutiae  of  no  real 
importance ;  such  for  instance  as  variations  in  the  thickness  of  rough  castings  or  unfin- 
ished forgings,  which  are  unavoidable,  and  deviations  from  symmetry  without  apparent 
reason,  which  may  be  due  to  inaccurate  workmanship.  Such  precise  duplication  is  rarely 
required.  In  making  any  part  of  a  machine  from  a  working  drawing,  in  ordinary  cases 
special  accuracy  is  necessary  in  regard  to  certain  dimensions  on  account  of  their  relation 
to  other  parts,  while  in  many  particulars  slight  deviations  from  the  drawing  may  be  of 
trifling  moment. 

The  object,  then,  is  usually  gained  if  the  original  drawing  can  be  reproduced  from 
the  sketch,  and  the  making  of  the  latter  is  greatly  facilitated  by  a  proper  distinction 
between  essentials  and  non-essentials. 

9.  Another  source  of  difficulty  is  the  fact  that  the  centre  lines,  which  in  the  drawing 
are  before   the   eye  and   often   furnish   a  key  to  the  laying  out   of  much   of  the   work,  do 
not  exist  in   the   finished   piece.     Consequently  the  beginner  is  apt  either  to  forget   them, 
or,  by  measuring   from   rough    surfaces,   or  similar    unreliable   methods,   to   fail    in   securing 
data    from    which   they  can    be    laid    down    in    correct    relation    to    each   other    or  to    some 
definite   base   line.     In   making  the  drawing,   the   very  first    step    is    to  locate  these    centre 
lines ;   and   so    in   making  the   sketch,   their   positions    should    be    determined    at    once,   and 
other  measurements  made    in   reference   to  them.     This  very  often  results  in  proving  with 
practical  certainty   that  parts  which   actually  are    not   symmetrical  about    these   lines  were 
intended  to    be    so,  the  observed   irregularities   being  due  to   errors  of  workmanship  or  to 
accidental  causes,  such  as  shifting  of  cores  or  prints,  unequal  contraction  of  castings,  and 
the  like :  in  which  case  the  labor  of  measuring  such   deviations  is  saved,  while  the  sketch 
itself  is  all  the  better. 


ON  FREE-HAND   SKETCHING.  51 

10.  Another  oversight  consists  in  omitting  to  verify  measurements  by  comparison  or 
otherwise,  to   make   sure   that   all   agree  with  each  other.     It  is  very  often   impossible  to 
take  a  necessary  dimension  directly,  and  it  must  be  reached   in  a  roundabout  manner,  by 
making  several  different  ones  and  then  adding  some  and  subtracting  others.     This  being 
done  for  this-  specific  purpose  ;  it  may  also  occur  that  in  measuring  other  parts,  a  second 
set  of  figures  is  obtained    by  manipulation  with  which   the  same  dimension  can  be  ascer- 
tained.    Now,  it  is  very   disagreeable,    on    attempting   tc    work    from    the    sketch,   to    find 
these  results  at  variance  with  each  other :  this  should  be  found  out  before,  and  the  error 
corrected.      And  it   hardly  need   be  added   that   care  should  always  be  taken  to  see  that 
the   sum  of   a   number  of  consecutive   dimensions    is   equal   to   the   actual   total   as   deter- 
mined by  measurement. 

11.  In  regard  to  the  number  of  dimensions   to   be   taken,  there   are  errors  of  redun- 
dance as  well  as  of  deficiency.     Beginners  not  only,  but  occasionally  those  of  considerable 
experience,   will   sometimes  cover  a  sketch   with   superfluous   figures,  and    sometimes   they 
do  not  put  down  enough.     Of  the  two,  the  former  is  preferable,  as  being  on  the  safe  side, 
always  provided  that   there  are  no   discrepancies ;    it  is  better  to  waste  the  time  required 
to  make  a  dozen  useless  measurements,  than  to  run  the  risk  of  omitting  one   that   may 
prove  essential — for   an   opportunity  may  not   offer  to   do   the  work  over  again,  and   if  a 
figure  be  lacking  it  is  tolerably  certain  to  be  among  the  first  ones  wanted  in  laying  out 
the  drawing. 

12.  The  novice  is  often  at  a  loss  to  decide  what  views  ought  to  be  sketched,  and  how 
they  should  be  arranged  in  relation  to  each  other. 

This  matter  is  determined  precisely  as  in  the  case  of  the  original  working  drawings;  the 
sketches  are  complete  only  when  they  contain  all  the  data  which  are  requisite  in  laying  out  a 
drawing  from  which  new  pieces  could  be  made  with  the  certainty  that  they  could  be  sub- 
stituted for  those  measured. 

And  be  it  observed  that  the  evils  of  a  slavish  observance  of  the  laws  of  projection,  great 
enough  in  making  drawings,  are  still  more  pronounced  in  the  making  of  sketches.  All  that 
has  been  said  in  regard  to  the  former  applies  with  added  emphasis  to  the  matter  now  under 
consideration :  by  following  the  suggestions  contained  in  the  preceding  chapters,  sketches 
may  be  kept  free  from  a  vast  amount  of  useless  rubbish,  the  introduction  of  which  is  a 
sinful  waste  of  valuable  time. 

13.  As  previously  remarked,  this  matter  cannot  well  be  reduced  to  the  form  of  abstract 
rules  of  procedure.     Two  or  three  general  principles,  however,  may  be  deduced  from  what  has 
been  set  forth,  which  apply  in  nearly  all  cases. 

(1)  Special  care  is  requisite  in  measuring  those  portions  of  any  detached  pieces  which  are 
fitted  to  other  parts  of  the  machine. 

(2)  Centre  lines  and  lines  of  symmetry,  when  such  exist,  should  be  carefully  located. 

(3)  All  measurements  should  be  made  from  centre  lines  or  faced  surfaces  when  possible. 

(4)  Measurements  should  be  verified  by  comparison,  and  all  discrepancies  corrected. 

14.  It  is  very  desirable  that  sketches  from  measurement  should  be  reasonably  compact ; 
and  by  skilful  management  it  will  be  found  practicable  to  make  distinctly  figured  and  com- 
plete free-hand  records  of  even  massive  machinery  on  the  pages  of  a  pocket  note-book. 

It  is  not,  however,  to  be  supposed  that  this  can  be  accomplished  if  all  parts  are  drawn  in 


PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 


due  proportion  and  upon  the  same  scale.  Nor  is  it  imperative  that  anything  approaching  to 
this  should  be  attempted  ;  if  it  can  be  done,  as  has  already  been  stated,  it  is  well  to  do  it ; 
but  if  not,  such  liberties  may  be  taken  with  the  proportions  as  circumstances  may  dictate. 

This  can  best  be  made  clear  by  example,  as  no  general  rules  can  be  laid  down  for  this 
either:  and  the  following  figures,  which  are  fac-similes  of  fair  free-hand  sketches,  are  given 
with  the  view  of  illustrating  to  some  extent  not  only  what  may  be  done  in  this  respect,  but 
some  other  points  previously  alluded  to,  as  well  as  one  or  two  which  have  not  been  mentioned. 

SKETCH  No.  i. 

15.  In  Fig.  41  is  shown  a  valve-stem  for  a  large  engine,  with  a  circular  collar  fitted  to  a 
conical  portion  of  the  stem  near  the  middle :  both  ends  are  threaded  and  provided  with  nuts. 

In  such  a  case  as  this,  the  diameter  may  be  exaggerated  and  the  length  contracted ;  as 
otherwise  the  sketch  would  be  inconveniently  long,  or  else  so  narrow  that  the  figures  could 


~x 


FIG.  41. 

not  be  distinctly  written  in.  This  is  equivalent  to  drawing  the  lengths  by  one  scale  and  the 
breadths  by  another,  a  familiar  expedient  in  topographical  work.  But  here  it  is  not  necessary 
to  preserve  the  proportions  which  actually  exist  between  the  different  parts  into  which  the 
total  length  is  divided. 

The  collar  is  shown  in  section  in  its  proper  place,  and  an  end  view  of  it  is  also  given  at 
the  right.  The  valve-stem  being  turned,  and  the  nuts  hexagonal,  no  other  view  of  either 
is  necessary. 


FIG.  42. 
SKETCH  No.  2. 

16.   A  simple  bridge-piece,  of  rectangular  section,  with  a  notch  cut  in  one  side  of  the 
raised  part,  and  a  bolt-hole  in  each  end,  is  shown  in  Fig.  42. 


ON  FREE-HAND   SKETCHING. 


S3 


This  is  a  case  in  which  a  single  view  is  sufficient,  when  drawn  in  oblique  projection,  or 
what  is  known  as  "  cavalier  perspective."  It  is  not  properly  perspective,  however,  as  the 
oblique  lines,  representing  those  lines  of  the  object  which  are  in  space  perpendicular  to  the 
plane  of  the  paper,  are  parallel  instead  of  convergent. 

This  method  is  often  extremely  convenient,  when  applied  as  in  this  case  to  objects 
bounded  by  lines  and  planes  at  right  angles  to  each  other. 

It  conveys  the  meaning  very  clearly,  and  the  drawing  may  be  worked  from  directly,  since, 
all  the  oblique  lines  being  parallel,  and  those  which  are  equal  always  appearing  equal,  they 
may  be  set  off  in  their  true  lengths  when  a  scale  is  used,  and  the  actual  dimensions  may  with 
perfect  propriety  be  written  on  a  sketch  thus  made. 


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FIG.  43. 

SKETCH  No.  3. 

17.  A  lever,  of  which  the  two  arms  make  an  obtuse  angle,  and  one  is  bent  at  right  angles, 
so  that  its  pm  is  parallel  to  the  shaft,  is  shown  in  Fig.  43. 


54 


PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 


Two  views  suffice  to  define  the  construction  of  this  somewhat  crooked  piece,  so  that  no 
questions  need  be  asked. 

In  the  end  view  on  the  right,  the  bent  arm  is  placed  with  its  centre  line  vertical ;  the 
other  arm  is  shown  in  its  true  length  and  position,  and  both  pins  are  drawn  in  section,  thus 


FIG.  44. 

avoiding  the  necessity  of  showing  the  outward  collars  and  dotting  the  pins.  This  last  item  is 
more  important  than  it  perhaps  seems,  as  the  pins  are  the  more  prominent  parts,  and  by  thus 
making  them  conspicuous  the  whole  is  rendered  more  clear  and  striking. 


ON  FREE-HAND   SKETCHING.  55 

In  the  side  view,  the  inclined  lever  is  not  projected  in  its  true  position,  but  is  shown  in  its 
true  length,  just  as  though  in  the  end  view  its  centre  line  were  also  vertical. 

Particular  attention  is  called  to  the  circumstance  that  in  this  view  vertical  centre  lines 
are  drawn  through  the  middle  points  of  the  lengths  of  the  pins  ;  and  the  distance  of  these 
from  each  other,  and  of  each  from  the  face  of  the  central  hub  of  the  lever,  are  given. 

These  vertical  lines  locate  the  planes  of  rotation,  and  their  positions  in  drawings  of  other 
parts  of  the  machine  which  are  connected  with  these  pins  must  obviously  agree  with  those 
here  shown. 

SKETCH  No.  4. 

18.  In  Fig.  44  are  shown  a  "  lifting  toe,"  and  its  cam  or  "  wiper,"  such  as   are  used  in 
the  valve  gear  of  the  common  beam-engine. 

On  the  left  there  is  sketched  a  side  view  of  these  two  pieces,  with  a  portion  of  the  lifting 
rod  to  which  the  toe  is  attached.  Above  this  'is  a  top  view  of  the  toe,  the  lifting  rod  being 
given  in  section  as  though  cut  off  above  the  toe.  Below  it  is  shown  a  top  view  of  the  wiper, 
a  section  of  the  lifting  rod  being  also  placed  in  its  proper  position  relatively  to  the  wiper,  a 
part  of  whose  rock-shaft  is  likewise  given  :  a  section  of  the  latter  is  seen  in  the  side  view. 

The  form  of  the  curved  face  of  the  wiper  is  important  ;  and  in  order  to  define  it  with 
precision,  an  enlarged  sketch  of  it  is  made  on  the  right.  In  this,  a  chord  of  the  curved 
acting  face  is  drawn,  and  the  "  offsets,"  or  perpendicular  distances  from  this  chord  to  the 
curve,  are  given  at  definite  intervals. 

This  chord  at  one  extremity  cuts  the  outer  circumference  of  the  hub  of  the  wiper:  and  in 
order  to  define  the  angle  at  which  the  wiper  is  placed,  a  line  is  drawn  from  the  other  extremity 
of  the  chord  through  the  centre  of  the  shaft;  also  a  perpendicular  to  this  line,  passing  through 
the  centre  and  cutting  the  circumference,  in  another  point  :  and  the  distance  from  this  last 
point  to  the  first-mentioned  extremity  of  the  chord  is  figured  in. 

SKETCH  No.  5. 

19.  The  subject  of  this  sketch  is  the  cross-head  of  a  steam-engine,  formed  of  a  transverse 
piece  forged  on  the  piston-rod,  which  is  also  shown  in  Fig.  45. 

Two  views  are  in  this  case  also  made  to  serve  all  purposes.  In  the  side  view  the  length 
of  the  piston-rod  is  contracted,  it  being  quite  needless  to  show  it  in  due  proportion  to  the 
other  parts.  And  while  the  idea  of  the  general  contour  of  the  cross-head  is  reasonably  well 
indicated,  no  attempt  has  been  made  to  preserve  the  relative  sizes,  which  are  sketched  so  as 
to  accommodate  the  figuring,  upon  which  everything  ultimately  depends  in  making  a  draw- 
ing to  scale. 

In  the  end  view,  the  piston-rod  is  shown  in  section,  and  so  also  is  a  part  of  the  upper  end 
of  the  cross-head,  the  lower  part  being  drawn  in  elevation.  Here,  again,  everything  is  made 
subservient  to  the  easy  and  clear  introduction  of  the  figures,  and  to  the  keeping  of  the  whole 
sketch  within  due  limits  as  to  size. 

SKETCH  No.  6. 

20.  In  Fig.  46  is  shown  a  pillow-block,  or  bracket,  of  a  somewhat  peculiar  form,  the  cap 
being  inclined  at  an  angle  of  45°  to  the  horizontal. 


UHI7BRSIT7 


PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 


ON  FREE-HAND  SKETCHING.  57 

In  such  a  case  as  this,  it  is  at  once  apparent  that  while  the  front  view  is  in  the  highest 
degree  explanatory,  a  view  from  either  the  right,  the  left,  or  above,  would  be  not  only  trouble- 
some to  sketch,  but  of  very  little  service  in  the  way  of  imparting  information,  if  it  were 
made. 

But  drawing  a  centre  line  perpendicular  to  the  cap,  it  is  equally  clear  that  a  direct  view 
of  the  bearing  from  the  upper  side,  in  the  direction  of  that  line,  will  convey  all  that  is  lacking 
as  to  the  construction  of  the  brasses  and  the  solid  metal  by  which  they  are  surrounded ;  the 
cap  may  be  omitted,  if,  as  is  usual  and  as  here  supposed,  its  outline  be  the  same  as  that 
of  the  bearing.  This  view  is  made  more  distinct  by  supposing  the  upper  brass  to  be  removed, 
and  showing  a  section  of  the  lower  one,  as  though  a  film  had  been  planed  off  its  upper  face. 

The  centre  lines  of  the  bolts  are  drawn  and  the  distance  between  them  given :  which  is 
sufficient,  as  when  there  is  no  indication  to  the  contrary,  it  is  always  understood  that  they  are 
equidistant  from  the  main  centre  line ;  and  the  same  holds  true  in  regard  to  other  dimensions, 
such  as  the  breadth  of  the  bearing,  the  diameter  of  the  bore,  the  width  of  the  brasses :  when 
practicable,  the  whole  should  be  given,  as  in  this  illustration,  and  not  the  halves,  or  distances 
from  the  centre  line. 

21.  But  when,  as  in  the  side  view,  the  main  centre  line  (in  this  case  the  vertical  one)  is 
not  a  line  of  symmetry  for  all  parts,  then  the  unequal  distances  from  it  to  those  lines  which  it 
is  necessary  to  locate  should  be  given :  as  for  instance  the  centre  lines  of  the  holding-down 
bolts. 

Now,  the  base  of  this  bracket  being  horizontal,  a  top  view  of  it  is  essential.  But  in  order 
to  avoid  the  introduction  of  a  foreshortened  view  of  the  bearing,  cap,  etc.,  the  upper  part  is 
cut  off,  by  the  two  horizontal  planes  ab,  cd ;  and  then  looking  perpendicularly  down  upon 
what  is  left,  a  perfectly  clear  idea  is  gained  of  the  structure  of  the  supporting  ribs  and  of  the 
whole  arrangement  of  the  base,  the  facing  strips  on  the  bottom  being  dotted  in.  From  this 
faced  surface  the  vertical  distance  to  the  centre  line  of  the  shaft  is  measured. 

In  sketching  such  an  arrangement  as  this,  there  is  no  reason  for  deviating  from  the  true 
proportions  as  they  actually  exist,  since  all  the  parts  are  so  compact  that  there  is  no  necessity 
to  reduce  any  one  of  them  for  the  sake  of  economizing  space,  nor  is  there  any  for  enlarging 
others  in  order  to  make  the  figures  clear. 

Opportunities  of  this  nature  should  always  be  improved  for  the  purpose  of  gaining  prac- 
tice and  skill  in  accurate  free-hand  drawing,  and  as  much  care  taken  as  time  will  permit  to 
sketch  in  proportion,  for  reasons  already  explained. 

SKETCH  No.  7. 

23.  In  Fig.  47  are  shown  all  the  sketches  necessary  for  the  barrel  of  an  air-pump  for  a 
marine  engine  provided  with  surface  condensers. 

This  is  very  different  from  the  preceding  subject  in  respect  to  the  possibility  of  sketch- 
ing in  proportion ;  the  diameter  and  the  length  being  so  great,  as  compared  with  the  thickness 
of  the  metal,  the  breadth  of  the  flanges,  and  the  sizes  of  the  bolts,  that  any  attempt  to  show 
the  whole  in  correct  relations  would  be  preposterous. 

Therefore  the  effort  is  not  made.  A  longitudinal  section  is  absolutely  necessary,  and 
the  thickness  of  metal  in  different  parts,  as  well  as  the  joints  and  fastenings,  must  be  clearly 
shown. 


PRACTICAL  HINTS  FOR   DRAUGHTSMEN. 


Now,  the  barrel  of  the  pump  is  round,  and  it  has  a  curved  nozzle  or  discharge-pipe,  of 
rectangular  section,  on  one  side  near  the  top.     The  bore  of  the  pump,  and  the  number  and 


FIG.  47. 

arrangement  of  the  bolts  in  the  flanges,  are  fully  indicated  by  making  a  top  view  of  a  little 
more  than  one  quadrant,  with  a  little  more  than  a  half  of  the  rectangular  discharge-pipe  just 
mentioned.  This  view  is  sketched  on  a  small  scale  in  the  lower  part  of  Fig.  47 :  or  rather 


ON  FREE-HAND   SKETCHING. 


59 


the  central  part,  for  below  this  top  view  is  given  an  outside  view  of  the  upper  part  of  the 
barrel,  including  the  upper  flange  and  the  discharge-pipe ;  showing  clearly  that  this  last 
extends  only  to  the  main  centre  line,  and  also  exhibiting  a  hub  which  must  be  provided  for 
one  of  the  standing  bolts,  which  comes  directly  over  the  side  wall  of  the  nozzle. 


4-  -  -  6V 


FIG.  48. 

Above  these  is  made  a  sketch  on  a  much  larger  scale,  being  a  section  by  the  plane  ab ; 
but  a  section  only  of  that  side  on  which  the  discharge-pipe  is  placed :  the  form  of  the  section 
of  the  opposite  side,  in  so  far  as  it  is  unlike  this  one,  is  indicated  by  continuing  the  side  wall 


60  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 

of  the  barrel,  above  the  lower  side  of  the  nozzle,  in  a  peculiar  style  of  dotted  line,  consisting 
of  alternating  dashes  and  dots. 

In  making  this  sectional  sketch,  all  the  flanges  and  bolts  are  indicated,  and  the  dimen- 
sions written  in :  the  length  is  contracted,  in  order  to  save  in  height ;  and  thus  the  whole  is 
fully  recorded  within  very  reasonable  limits  of  space. 

SKETCH  No.  8. 

In  Fig.  48  are  given  sketches  of  a  bracket  provided  with  three  bearings.  In  the  first 
bearing  runs  a  vertical  shaft  having  at  its  lower  end  a  mitre-wheel,  which  engages  with  a 
similar  wheel  on  the  second  shaft ;  this  shaft  is  horizontal,  and  carries  also  a  spur-wheel  of 
70  teeth,  engaging  with  another  of  33  teeth  on  the  third  shaft,  which  is  parallel  to  the 
second. 

This  example  specially  illustrates  the  necessity  of  locating  centre  lines  with  reference  to 
each  other  and  to  faced  surfaces. 

As  clearly  shown  in  the  side  view  at  the  left,  this  bracket  has  a  faced  bearing  surface,  which 
is  to  be  bolted  against  its  support ;  and  the  first  step  should  be  to  measure  the  exact  distance 
of  the  vertical  axis  from  this  face :  the  second,  to  measure  the  distance  of  the  lower  horizontal 
axis  below  the  lower  edge  of  the  same  faced  surface.  From  these  centre  lines  are  measured 
the  distances  to  the  faces  of  the  two  bearings  shown  in  that  view ;  and  the  two  mitre-wheels 
are  indicated  by  dotting  in  the  pitch  cones  and  marking  the  numbers  of  their  teeth. 

The  centre  line  of  the  third  shaft  is  located,  as  shown  in  the  front  and  top  views,  by 
measuring  its  distance  to  the  right  of  the  plane,  of  the  other  two,  and  also  its  distance  above 
the  lower  horizontal  axis,  a  good  check  being  to  measure  in  addition  the  direct  distance 
between  the  two  horizontal  axes. 

The  bearing  of  this  third  shaft  is  fully  shown  in  the  two  views  at  the  right,  and  therefore 
is  not  dotted  in,  in  making  the  side  view  at  the  left ;  similarly,  the  lower  horizontal  bearing, 
being  completely  defined  in  the  two  lower  views,  is  omitted  in  the  top  view:  it  being  a  gen- 
eral principle  to  avoid  dotted  lines  whenever  they  can  be  dispensed  with. 

The  pitch  circles  of  the  two  spur-wheels  are  shown  in  the  front  view  at  the  right :  and 
the  numbers  of  teeth  being  noted,  this  sketch  contains  a  complete  record  of  the  system  of 
gear-wheels  used,  so  far  as  the  velocity  ratios  are  concerned :  which,  though  not  essential  to 
the  completeness  of  the  bracket,  is,  nevertheless,  useful  information,  as  indicating  the  manner 
in  which  the  wheels,  which  would  be  sketched  separately,  are  to  be  arranged. 

SKETCH  No.  9. 

In  Fig.  49  are  shown  sketches  of  a  "  stationary  link"  such  as  is  sometimes  used  as  a 
reversing  gear  for  steam-engines,  with  the  link-block  and  valve-rod. 

This  link  consists  of  a  slotted  arc,  connected  by  means  of  two  short  standards  to  a  curved 
back-piece  which  is  extended  into  a  lever,  and  secured,  by  means  of  a  hub  formed  upon  it,  to 
a  supporting  spindle.  The  forms  of  the  arc  and  the  back-piece  are  clearly  shown  in  the 
upper  view  at  the  left :  the  supporting  spindle  and  the  standards  are  shown  in  the  side  view, 
at  the  right,  where,  however,  the  lever  is  not  dotted  in,  as  it  would  present  a  confused  and 
confusing  mass  of  dotted  lines. 

In  order  to  show  this  lever  and  its  pin,  a  top  view  is  given  below,  in  which  the  back-piece 


ON  FREE-HAND  SKETCHING. 


61 


is  cut  off,  not  through  the  centre,   but  above  the  hub.     The  link  itself,  however,  is  cut  by 
the  horizontal  plane  ab,  in  this  top  view;  so  also  is  the    link-block,  which  is  here  supposed 


62  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 

to  be  in  its  central  position,  although  in  the  front  view  above  it  is  pushed  half  way  up  to  its 
highest  position  for  the  sake  of  perspicuity. 

In  the  top  view  also  the  valve-rod  is  shown,  with  its  pin,  but  neither  of  them  in  section: 
and  finally,  a  front  view  of  the  valve-rod  without  the  pin  is  given  below. 

The  angular  movement  of  the  lever  and  the  link  is  indicated  by  dotting  in  the  arcs,  and 
the  radii  limiting  the  extreme  positions  of  the  lever-pin,  and  of  the  link-block  pin,  in  both 
the  lowest  and  the  highest  positions.  Also  the  angular  movement  of  the  valve-rod  in  going 
from  "  full  ahead  "  to  "  full  back"  is  similarly  indicated  by  dotting  the  centre  lines  for  those 
two  positions,  the  centres  of  the  pins  being  indicated  by  minute  circles :  and  thus  the  sketch 
conveys  a  very  clear  idea  of  the  nature  and  extent  of  the  movements  for  which  the  arrange- 
ment is  designed. 

The  dimensions  of  all  the  smaller  details  are  not  given  in  this  sketch ;  but  attention  is 
called  to  the  arrangement  and  location  of  the  figures  which  are  given ;  which  will  on  exami- 
nation be  found  sufficient  for  laying  out  the  link  and  the  principal  pieces  connected  with  it. 

These  few  examples  will  serve  to  illustrate  some  of  the  most  important  points  to  be 
observed  in  making  sketches  of  details,  the  nature  of  the  expedients  which  may  be  resorted 
to  on  occasion  for  abbreviating  the  work  and  saving  space,  as  well  as  the  style  in  which  they 
can  be  executed  with  the  free  hand  when  the  object  is  to  preserve  the  due  proportions  of  the 
parts. 

It  is  to  be  understood  also,  that  the  methods  of  representation  set  forth  in  the  two 
preceding  chapters  are  just  as  applicable  in  sketching  as  in  drawing  to  scale,  and  many 
useful  hints  may  be  found  in  the  illustrations  there  given. 

In  conclusion  it  may  be  well  to  observe,  that  while  skill  in  free-hand  work  pure  and 
simple  is  a  most  valuable  accomplishment,  the  acquirement  of  which  cannot  be  too  strongly 
advised  ;  yet  the  inference  must  not  be  drawn  that  in  "  sketching  from  measurement"  the 
size  of  instruments  is  under  all  circumstances  prohibited. 

It  often  happens  that  time  is  of  the  utmost  consequence,  and  measurements  and  records 
are  required  in  such  haste  that  he  who  makes  them,  if  not  already  an  expert,  cannot  in  con- 
science avail  himself  of  the  task  to  train  his  unskilled  hand.  In  such  event,  although  a 
scale  cannot  well  be  used,  the  ruler  and  the  compasses  may  and  should  be  employed  :  but 
with  the  mental  resolution  that  the  necessity  for  so  doing  shall,  at  the  earliest  possible 
moment,  cease  to  exist. 


DRAWING  INSTRUMENTS  AND  MATERIALS. 


CHAPTER   IV. 

DRAWING   INSTRUMENTS  AND   MATERIALS. 

1.  A  great  number  of  appliances  can  be  packed  into  a  case  of  instruments,  if  it  is  only 
large  enough ;  and  a  whole  treatise  might  be  devoted  to  an  explanation  of  them.     Many  of 
those  found  in  the  more  expensive  cases,  though  each  has  ostensibly  a  purpose,  are  in  fact  of 
pecuniary  value  only,  and  of  no  practical  use  whatever ;  notwithstanding  which  they  are  very 
often  given  such  prominence  even  in  works  upon  drawing  as  to  imply  that  their  possession  is 
desirable.     It  is  proposed  here  to  describe  only  those  instruments  which  are  essential  for  the 
ordinary,  and  sufficient  for  the  extraordinary,  occasions  of  the  mechanical  draughtsman  ;  and 
to  add  some  hints  as  to  their  selection,  for  the  guidance  of  those  whose  judgment  has  not 
been  trained  by  experience,  because  the  difference  between  a  good 

article  and  one  which  is  radically  bad  often  lies  not  in  the  quality 
or  finish,  but  in  points  which  might  be  easily  overlooked  by  any 
one  not  an  expert  in  its  use. 

In  this  as  in  many  other  matters  true  economy  consists  in 
procuring  the  best.  There  is  a  vast  amount  of  "  cheap  "  trash  in 
the  shops,  and  he  who  is  wise  will  leave  it  there.  If  he  has  but 
a  limited  sum  at  command,  his  best  course  is,  not  to  buy  a  "  com- 
plete set"  of  inferior  quality,  but  to  purchase  only  what  is  abso- 
lutely indispensable  at  the  time,  and  add  to  his  stock  subse- 
quently as  opportunity  permits. 

The  English,  French,  Swiss,  and  German  instruments  have 
each  their  distinguishing  characteristics  of  style,  in  regard  to  the 
beauty  of  which  tastes  differ ;  but  this  is  not  a  thing  of  material 
consequence.  But  there  are  features  which  are ;  and  instruments 
of  whatever  make  should  possess  certain  qualities  in  order  to 
give  perfect  satisfaction  in  use.  Some  of  those  mentioned  are 
almost  always  excessively  heavy,  and  this  is  not  good ;  every 
piece  should  be  as  light  as  is  consistent  with  the  necessary  stiff- 
ness and  freedom  from  springing.  The  illustrations  that  follow 
represent  instruments  of  the  English  pattern,  but  lighter  than 
those  of  English  make  are  usually  found ;  the  exact  proportions 
having  been  determined  by  experiment,  the  weight  being  gradu- 
ally reduced  until  the  present  limit  was  reached.  They  are  of 
American  manufacture,  and  in  every  respect  equal  to  any  in  the 
world. 

2.  The  Dividers. — Beginning  with  the  "  case  instruments,"  the  first  thing  on  the  list  is  a 
pair  of  dividers,  Fig.  50.     The  construction  of  this  is  too  familiar  to  require  explanation.     The 
lower  part  of  the  leg  is  of  fine  steel,  the  upper  part  preferably  of  German  silver.     The  body 


FIG. 


PRACTICAL  HINTS  FOR  DRAUGHTSMEN. 


of  the  leg  is  of  triangular  form,  but  for  half  an  inch  at  the  lower  end  is  made  round,  forming 
what  is  known  as  the  English  needle-point.  The  points  should  close  fairly  together;  they 
should  be  as  sharp  as  needles,  and  kept  so :  their  use  is  not  to  act  as  a  nut-pick,  a  drill,  or  a 
reamer,  as  sometimes  erroneously  supposed,  but  to  make  the  finest  of  visible  holes  in  the  sur- 
face only  of  the  paper. 

The  value  of  the  instrument  depends  upon  the  perfection  of  the  joint.  This  should  be 
so  accurately  fitted  as  to  move  with  uniform  ease  through  the  whole  range  of  its  motion ;  if  it 
goes  easily  in  one  place  and  sticks  in  another,  or  if  in  either  opening  or  closing  from  any  posi- 
tion the  legs  resist  at  first  and  yield  with  a  start,  the  instrument  is  a  poor  one,  let  the  maker 
be  who  he  may. 

The  best  form  of  joint  is  that  shown  in  the  figure,  and  known   as   the   "  double   sector 

joint,"  the  upper  part  of  one  leg  being  provided 
with  two  thin  leaves  of  steel,  fitting  into  two  slots 
in  the  other  leg.  This  requires  the  best  of  work- 
manship, but  a  good  joint  of  this  kind  will  last  in- 
definitely, and  its  use  is  a  constant  pleasure. 

In  selecting,  the  joint  should  be  tested  as  in 
using;  it  should  retain  any  position  without  the 
least  "  shakiness,"  but  move  with  such  ease  that  it 
can  be  opened  to  its  full  range  with  the  fingers  of 
one  hand  only,  and  adjusted,  or  set  to  any  given 
measurement,  with  perfect  facility  in  the  same 
manner. 

The  most  convenient  length  for  ordinary  use  is 
about  five  inches,  and  a  pair  of  this  size  should 
form  a  part  of  every  set  of  instruments :  if  there 
be  another  pair,  a  length  of  from  three  and  one 
half  to  four  inches  will  be  found  very  convenient 
when  making  drawings  on  a  small  scale. 

3.  The  Compasses. — As  above  stated,  the 
dividers  are  used  for  setting  off  measurements  by 
pricking  the  surface  of  the  paper ;  they  are  never 
used  for  describing  circles.  The  instrument  for 
this  purpose  is  a  pair  of  compasses,  Fig.  51.  The 
form  and  construction  are  the  same  as  in  the  di- 
viders, except  that  one  leg  is  jointed,  and  the  other 
leg  is  fitted  with  three  "shifting  points,"  viz.,  a 
plain  leg,  a  pen,  and  a  pencil-holder,  each  of  which 
is  also  provided  with  a  joint. 
These  joints  are  necessary  in  order  that  each  leg  when  in  use,  or  at  least  the  lower  part 
of  it,  may  be  placed  as  nearly  vertical  as  possible. 

A  great  many  are  to  be  found  with  joints  only  in  the  shifting  pieces,  the  other  leg  being 
rigid  like  that  of  the  dividers ;  these,  too,  have  their  proper  place,  and  that  place  is  in  the 
show-case  of  the  dealer's  shop. 


FIG.  51. 


DRAWING  INSTRUMENTS  AND  MATERIALS.  65 

The  principal  joint  (that  uniting  the  legs)  is  made  the  same  as  in  the  dividers,  and  the 
same  tests  should  be  applied  to  it  in  selecting;  the  joints  in  the  leg  and  shifting  pieces  are 
also  best  made  double,  two  leaves  of  steel  fitting  between  three  of  German  silver ;  they  should 
move  with  uniformity  throughout,  but  rather  less  easily  than  the  main  joint :  they  are  more 
liable  to  disarrangement  in  handling,  and  nothing  is  more  vexatious  than  compasses  which  are 
"  weak  in  the  knees." 

4.  The   Needle-point  with   which   the    permanent   leg  of  the   compasses   is    provided 
should  be  most  carefully  scrutinized.     The  point  itself  is  separate  from  the  leg,  and  consists 
merely  of  a  piece  of  finely  tempered  steel  wire,  which  should  be  quite  thick,  tapering  to  a 
point  like  that  of  the  dividers  at  one  end ;  at  the  lower  end  a  square  shoulder  is  formed,  with 
a  very  fine  and  sharp  point  projecting  below  it.     This  point  only  should  enter  the  paper,  and 
the  object  of  the  shoulder  is  to  support  the  weight  of  the  instrument.     Hence  the  shoulder 
should  be  as  broad  as  the  diameter  of  the  wire  will  leave  it ;  and  on  no  account  should  the 
lower  end  of  the  wire  be  chamfered  or  tapered,  as  it  too  often  is. 

The  needle-point  enters  a  cylindrical  socket  in  the  lower  end  of  the  leg  of  the  com- 
passes, and  is  secured  by  a  set-screw.  It  should  enter  this  socket  with  a  snug  sliding  fit, 
without  side  shake,  and  be  of  such  length  that  the  set-screw  shall  bear  against  the  cylindrical 
and  not  against  the  tapered  part. 

There  is  another  form  of  needle-point,  in  which  a  socket  or  a  clamp  is  arranged  to  hold  a 
common  needle ;  which  is  mentioned  only  to  warn  the  reader  against  it  as  being  in  most  cases 
worse  than  none  at  all,  and  in  the  remainder  very  little  better. 

5.  The  best  mode  of  securing  the  shifting  points  in  place  is  by  means  of  the  "  bayonet 
joint,"  which  is  shown  in  the  figure.     The  lower  end  of  the  short  leg  to  which  they  are  fitted 
is  first  drilled  to  form  a  short  cylindrical  socket,  and  this  socket  is  then  sawed  through  for  a 
short  distance,  on  the  outside,  allowing  a  small  amount  of  spring. 

The  upper  end  of  each  shifting  point  is  turned  cylindrically  to  fit  the  socket,  and  pro- 
vided with  a  feather  on  the  outside,  which  enters  the  split  above  mentioned,  being  very 
slightly  tapered  to  secure  a  tight  and  reliable  fit.  This  is  far  more  neat,  compact,  and  con- 
venient in  use,  than  the  more  common  device  of  a  binding  screw  to  hold  the  shifting  pieces 
in  place. 

If  the  latter  is  used,  the  socket  and  the  neck  which  enters  it  should  be  square  in  section, 
and  should  fit  without  side  shake  before  the  binding  screw  is  tightened ;  also,  let  the  pur- 
chaser see  to  it  that  the  screws  are  long  enough,  and  have  heads  of  liberal  size. 

6.  The   Shifting   Points  are  three  in  number,  as  previously  stated,  viz. :  a  plain  leg,  a 
pen,  and  a  pencil-holder. 

The  plain  leg  is  formed  like  that  of  the  dividers,  and  like  it  terminates  in  an  English 
needle-point.  When  this  piece  is  used,  the  movable  needle-point  of  the  permanent  leg  may 
be  reversed,  when  the  whole  becomes  another  pair  of  dividers,  which  is  sometimes  very  con- 
venient. 

The  pen  is  formed  of  two  blades  of  steel,  through  one  of  which  an  adjusting  screw 
passes,  which  is  tapped  into  the  other ;  the  whole  being  precisely  like  the  drawing  pen  to  be 
more  fully  described  presently,  and  subject  to  the  same  scrutiny  and  criticism  in  selecting. 

The  pencil-holder  is  in  the  form  of  a  clamp,  consisting  of  a  small  tube,  which  is  either  a 
part  of  the  lower  piece  of  this  joint,  or  if  made  of  steel,  brazed  to  it  on  the  outside,  at  a  small 


66  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 

inclination  as  shown.  Both  tube  and  supporting  piece  are  split  longitudinally,  and  a  binding 
screw  on  the  side  gives  the  requisite  pressure. 

This  piece  should  be  most  carefully  scrutinized,  as  there  are  many  makers  who  seem  to 
think  that,  no  matter  what  the  proportions  or  arrangement,  a  clamp  is  a  clamp,  and  one  as 
good  as  another;  and  so  it  is  not. 

In  the  first  place,  the  tube  should  be  accurately  drilled,  so  that  a  Faber  "  instrument 
lead"  may  fit  it,  and  thus  receive  uniform  pressure  at  every  part  of  the  tube  when 
screwed  up. 

In  the  second  place,  in  order  to  produce  this  uniform  pressure,  the  binding  screw 
should  be  placed  opposite  the  middle  of  the  length  of  the  tube. 

In  the  third  place,  that  the  lead  may  be  held  with  sufficient  firmness,  the  tube  should 
be  from  one  half  to  three  fourths  of  an  inch  in  length,  according  to  the  size  of  the  in- 
strument. 

In  the  fourth  place,  the  lower  end  of  the  tube,  when  the  compasses  are  closed, 
should  be  at  least  five  sixteenths  of  an  inch  above  the  lower  end  of  the  needle-point  socket 
on  the  permanent  leg.  Thus  the  lead  will  project  about  three  eighths  of  an  inch  below  the 
tube ;  which  is  necessary  in  order  to  sharpen  it  properly. 

In  the  fifth  place,  the  head  of  the  binding  screw  should  stand  well  out  from  the 
bearing  surface,  be  of  liberal  size  and  thickness,  and  well  milled  on  the  edges.  And  the 
same  is  true  of  all  binding  screws  employed. 

7.  The   above   form    of  pencil-holder  is  beyond   question  and   beyond   comparison   the 
best  form.      There   is   another,  in   which    the   end   of   the  split   tube   is  made  conical,  and 
compressed  by  screwing  over   it  a   tube   correspondingly   tapered    internally.      The  whole 
is  precisely    the   same   device   as   that    used   for   securing   the  movable  leads   in   wood   or 
ivory   holders   for  writing;  which  purpose   it  answers  admirably.     But  its  application  to  a 
pair  of  compasses  is  the  climax    of  misdirected  ingenuity,   and  mention  is  made  of  it   for 
the  sole  purpose  of  cautioning  the  reader  against  it.     The  pencil  is   to  be  trimmed  to  an 
edge,  which  .must  be  tangent  to  the  arc  to  be  drawn;  and  after   trimming  it   is   usually  a 
little    too   short,    and    requires    to    be    drawn    out.      With    the    clamp    first    described,    this 
adjustment   can    be  readily  made,  nor   is   there  any   danger   of  disturbing   it  in  tightening 
the  binding  screw.      But  with   the  device  here  deprecated,  the  lead  is  almost  sure   to  be 
pushed  in,  and  what  is  worse,  turned    partially  around  ;    so  that    in  spite   of  its  neat   and 
plausible  appearance,  it  is  practically  as  bad  an  arrangement  as  could  be  adopted. 

Another  useless  piece  of  furniture  is  ordinarily  added  to  the  compasses.  This  is  the 
"  lengthening  bar ;"  which  is  a  bar  of  metal,  one  end  fitted  to  enter  the  socket  of  the 
short  leg,  the  other  furnished  with  a  similar  socket,  to  receive  the  pen  or  pencil.  The 
object  is  to  increase  the  range  and  permit  large  circles  to  be  drawn  :  a  good  object,  but  a 
bad  expedient.  For  with  this  addition  the  instrument  is  apt  to  spring  unless  excessively 
heavy :  a  beam  compass  is  much  better. 

8.  The   compasses,  if   there   be  but   one   pair  in   the  case,    will   be   best   adapted    for 
general  use  if  about   five  and  a  half  inches  in  length.     If  larger  they  are  too  heavy,  since 
in   order   to  prevent   springing  the   weight   must   be   increased  in  a  more  rapid  ratio  than 
the  length. 


DRAWING  INSTRUMENTS  AND   MATERIALS.  67 

Smaller  ones  are  extremely  serviceable ;  and  a  pair  of  four  inches  in  length,  made 
upon  exactly  the  same  lines,  will  soon  come  to  be  highly  prized  by  the  possessor;  being 
more  convenient  than  the  larger  ones  for  drawing  circles  a  little  beyond  the  range  of  the 
spring-bows,  and  for  general  use  in  making  drawings  on  a  small  scale. 

9.  The   Drawing  Pen. — This  instrument,  as  shown   in  Fig.  52,  consists   merely  of  two 
rather  stiff  blades   of    steel,  formed    out    of    one    piece.      Their    elasticity   keeps 

them  apart,   the  distance  being  adjusted  by   means   of   the   screw,   which    passes 
through  one  blade  and  is  tapped  into  the  other. 

This  is  the  best  form,  although  its  first  cost  is  least.  Many  pens  are  made 
with  the  outer  blade  hinged  to  the  inner  one,  the  two  being  kept  apart  by  a 
spring.  The  ostensible  advantage  is  the  facility  of  cleaning  them :  which  is 
no  real  advantage,  because  there  is  no  difficulty  in  cleaning  the  others.  The 
jointed  pens  cost  more,  and  are  not  as  good  ;  because  the  least  wear  will  permit 
a  sliding  movement  of  one  blade  over  the  other,  which  renders  their  action 
uncertain. 

The  inner  edge  of  the  blade  into  which  the  screw  is  tapped  should  be 
straight,  and  in  line  with  the  axis :  the  outer  blade  should  be  so  curved,  as  in 
the  figure,  that  the  two  shall  approach  each  other  most  rapidly  toward  the 
point.  The  object  is  to  have  a  reasonable  quantity  of  ink  retained  there,  so 
that  it  will  not  evaporate  too  quickly,  as  it  would  if  the  film  were  thin.  The 
blades  should  be  comparatively  broad,  and  well  rounded,  at  the  points,  as  then 
they  will  not  wear  so  rapidly,  and  will  remain  longer  in  condition  to  make 
smooth  lines,  than  if  they  taper  to  a  narrow  point.  In  selecting,  they  should 
always  be  tested  to  see  that  they  are  properly  set,  and  have  no  tendency  to 
cut  or  to  scratch  the  paper.  The  case  should  contain  at  least  two,  and  pref- 
erably three,  pens  of  different  sizes,  the  smaller  being  used  for  the  finer  lines. 

With  proper  care  and  usage,  the  pen  will  remain  for  a  long  time  in 
good  working  order.  It  should  be  held  as  nearly  vertical  as  possible,  that 
the  blades,  when  they  do  wear,  may  wear  "  square  across."  For  wear  they 
will,  and  occasionally  require  to  be  reset :  and  if  by  habitually  inclining  the 
pen  the  blades  are  thus  worn  off  obliquely,  the  film  of  ink  in  contact  with 
the  paper  will  be  bounded  by  converging  instead  of  parallel  lines,  and  when  this  is  the 
case  to  any  appreciable  extent  the  line  drawn  will  be  no  longer  smooth  and  even, 
but  ragged  and  rough.  The  sharpening,  or  "  setting,"  is  effected  by  means  of  a  small 
fine  oilstone,  and  the  secret  of  success  is  best  learned  from  the  instrument-maker.  If 
the  draughtsman  in  constant  employment  cannot  sharpen  his  own  pens,  it  is  a  good 
plan  to  have  an  extra  set  of  them,  that  he  may  always  have  those  serviceable  which 
are  in  use. 

10.  The   Spring-bows.      For  the  smallest  work  there   must    be   smaller   instruments: 
and  the  "spring-bows."  Figs.  53.  54,  and  55.  are  adapted  to  the  drawing  of  very  small  circles, 
and  the   subdivision   and   setting  off  of  minute  distances.      The   legs  of   these,  instead  of 
being  jointed  together,  are  formed  of  one  piece  of  steel,  the  elasticity  keeping  them  apart. 
and  the  radius  being  adjusted  by  means  of   a  screw  pivoted   to  one  leg,  passing  through 
a   hole   in  the  other,   and   provided   with   a   milled  thumb-nut.     The  hole   in   the  outer  leg 


68 


PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 


must  be  large  enough  to  accommodate  the  motion  of  the  screw  as  the  angle  of  the  legs 
varies,  and  on  the  outside  should  be  of  spherical  form,  the  bearing  end  of  the  thumb- 
nut  being  correspondingly  convex,  in  the  manner  of  a  ball-and-socket  joint. 

In  all  these  little  instruments,  the  degree  of  stiffness  of  the  spring  is  of  paramount 
importance.  A  very  common  fault  is  the  making  of  the  legs  too  thin  at  the  top,  the 
result  being  a  tendency  to  tremble,  and  a  consequent  variation  of  the  radius,  often  even 
under  the  slight  pressure  required  to  draw  a  firm  clean  line  with  them.  If  there  be  the 
slightest  indication  of  such  weakness  at  any  part  of  the  range,  the  piece  should  be  per- 
emptorily rejected  ;  it  is  better  that  the  spring  be  a  little  too  stiff ;  but  there  is  not  much 
latitude  in  that  direction  either,  for  too  powerful  a  spring  causes  the  screw  and  nut  to 


FIG.  53. 


FIG.  54. 


FIG.  55. 


wear  out  rapidly,  and  renders  the  adjustment  difficult.  All  these  instruments  are 
manipulated  by  means  of  a  small  handle  at  the  top,  preferably  of  cylindrical  form,  and 
made  of  metal  very  finely  milled  to  give  a  firm  hold. 

11.  The  "  spacing  divider,"  as  it  is  often  called,  Fig.  53,  consists  merely  of  two  plain 
points;  these  should  be  as  sharp  as  steel  can  be  made,  and  kept  so;  and  capable  of  being 
screwed  up  so  that  the  extremities  will  meet. 

The  "  bow-pencil,"  Fig.  54,  has  one  leg  formed  into  a  clamp  for  a  Faber  instrument 
lead,  exactly  like  that  of  the  compasses.  The  tube  of  this  clamp  should  not  be  less  than 
three  eighths  of  an  inch  long;  and  the  other  leg  should  extend  at  least  the  same  distance 
below  the  lower  end  of  the  tube. 

Another  most  important  test  is  the  following :  Put  into  the  clamp  a  lead  truly  sharp- 
ened to  a  conical  point,  or,  better,  a  wire  of  the  same  size  thus  tapered,  and  close  the 
instrument.  These  two  points  should  come  exactly  together ;  if  they  do  not,  the  piece  is 
not  worth  accepting  as  a  gift,  unless  on  condition  that  the  recipient  may  in  turn  present 
it  to  a  rival.  In  other  words,  the  axis  of  the  tube  should  lie  in  a  plane  passing  through 
the  supporting  point  (or  centre  of  the  circle  to  be  drawn)  and  the  axis  of  the  handles. 


DRAWING   INSTRUMENTS  AND   MATERIALS.  69 

The  most  serious  fault  is  to  have  the  tube  inclined  to  that  plane  ;  and  the  next  to  that 
to  have  the  clamp  come  foul  of  the  opposite  leg  on  closing  the  instrument.  The  former 
renders  it  difficult  to  draw  a  circle  at  all ;  the  latter  renders  it  impossible  to  draw  the 
smallest  ones  :  both  are  very  common,  but  neither  is  excusable. 

To  do  the  best  work  with  this  instrument,  the  lead  must  be  carefully  trimmed  to  a 
clean  edge,  rounded  like  the  point  of  the  drawing  pen,  and  concave  on  the  inner  side  as  in 
the  figure ;  it  must  also  be  as  carefully  adjusted  so  as  to  lie  with  this  edge  tangent  to  the 
circle,  and  to  be  of  just  the  right  length.  All  of  which  can  best  be  done  with  the  form 
of  clamp  here  recommended. 

The  bow-pen,  Fig.  55,  has  one  leg  formed  into  a  pen,  which  is  exactly  similar  in  form 
to  the  drawing  pen,  Fig.  52.  The  peculiar  curvature  of  the  outer  blade,  to  which  attention 
was  called  in  (9),  is  most  important  in  thfs  small  bow,  because  when  set  to  a  very  small 
radius,  the  pen  cannot  be  cleaned  and  refilled  easily  without  opening  the  legs;  and  when 
a  large  number  of  such  little  circles  of  the  same  radius  are  to  be  drawn,  it  makes  a  great 
difference  in  time  whether  this  operation  must  be  repeated  once  in  five  minutes  or  once 
in  ten. 

The  bow-pen  should  be  carefully  tested  by  trial,  to  see  that  the  plane  of  tht 
edge  of  the  pen  is  tangent  to  the  circle ;  and  also  to  see  that  when  closed  the  opposite 
leg  shall  touch  the  inside  of  the  pen,  and  that  at  tlte  middle  of  the  breadth  of  the  blade. 

The  supporting  point  should  project  a  very  little  beyond  the  end  of  the  pen  or  the 
pencil,  so  as  just  to  puncture  the  surface  of  the  paper:  and  it  should  be  possible  with 
either  pencil  or  pen  to  draw  a  circle  of  one  thirtieth  of  an  inch  in  diameter,  or  even  less. 

12.  The  form  of  spring-bow  above  described   is  recommended  as  being  the  lightest  and 
most  convenient.     One  material  feature,  affecting  the  convenience,  remains  to  be  noted,  viz. : 
the  adjusting  screw  is  pivoted  to  the  pen  or  pencil  leg,  and  the  thumb-nut  bears  against  the 
opposite  leg.     This  is  of  especial  consequence  in  the  smaller  sizes,  and  more  important  in  the 
bow-pencil  than   in   the    bow-pen.     But    it    is    far   preferable   to    the   contrary  arrangement, 
adopted  by  many  makers.     For  in  that  arrangement  the  thumb-nut  is  in  the  way  of  the  pencil, 
unless  the  adjusting  screw  is  too  high  up  or  the  pencil-clamp  too  low  down  or  too  short — and 
very  often  all  these  faults  exist  at  once ;  and  again,  in  drawing  several  small  circles  without 
lifting  the  bow  from  the  paper,  the  instrument  being  held  on  the  centre  by  the  index-finger 
resting  on  the  top  of  the  handle,  the  thumb  and  middle  finger  are  used  in  changing  the 
radius ;  so  that  if  the  nut  is  over  the  pen  or  pencil  the  work  is  obscured  by  them. 

13.  If  there  be  but  one  set  of  bows,  a  very  convenient  size  is  one  inch  and  three  quarters 
in  length,  from  the  crotch  of  the  spring  to  the  point.     If  there  be  two  sets,  the  smaller  may 
be  one  inch  and  five  eighths,  the  other  two  inches,  in  length.     They  are  to  be  had  much 
larger  than  this ;  but  are  not  to  be  recommended,  as  too  wide  a  range  makes  the  adjustment 
tedious ;  besides,  those  larger  ones  are  not  suited  for  very  small  work,  and  anything  beyond 
the  range  of  the  size  first  "nentioned  can  readily  be  drawn  with  the  compasses. 

These  spring-bows,  it  is  to  be  observed,  may  be  and  often  are  provided  with  needle- 
points :  and  if  there  be  two  sets,  the  larger  ones  may  advantageously  be  thus  fitted ;  or  at 
least  the  ones  with  the  pen  and  the  pencil.  The  advantage  is  most  obvious  in  the  case  of  the 
pen  bow,  owing  to  the  necessity  of  some  adjustment  due  to  the  gradual  shortening  of  the 
pen  by  wear.  But  in  respect  to  the  wearing  of  a  hole  in  the  paper  when  many  circles  are 


70 


PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 


drawn  about  the  same  centre,  the  advantage  is  more  fancied  than  real,  if  the  operator 
handles  his  instruments  as  lightly  as  he  should.  And  in  drawing  very  small  circles  the 
needle-point  is  rather  in  the  way:  but  if  it  be  preferred,  by  all  means  let  the  sliouldered 
needle-point  be  chosen,  and  made  precisely  like  that  described  in  (4).  Except  of  course  in 
the  case  of  the  spacing  divider,  which  must  have  tapered  points  if  it  has  any. 

14.   Jointed   Bows. — The  above  are  the  essential  instruments ;  if  additional  facilities  for 
drawing  circles  are  desired,  a  jointed  bow-pen  and  bow-pencil,  Figs.  56  and  57.  may  be  added, 


FIG.  56.  FIG.  57. 

and  are  in  many  emergencies  very  useful.  They  are  exactly  similar  in  construction  to  the 
compasses,  (double-jointed  throughout,)  with  the  addition  of  a  handle  at  the  top,  a  jaw  at  the 
lower  end  of  which  embraces  the  mai.i  joint  of  the  instrument.  Thus  these  bows  are  manip- 
ulated like  those  before  described,  by  merely  twirling  the  handle  between  the  thumb  and 
finger. 

Bows  of  this  kind  should  not  be  more  than  about  two  and  a  half  inches  in  length  from 
the  point  to  the  centre  of  the  main  joint ;  for  if  much  longer,  they  cannot  be  well  controlled 
by  the  handle  at  the  top. 

And  it  may  be  added,  that  the  mere  existence  of  such  a  handle,  for  any  reason,  upon 
larger  compasses  or  dividers,  is  a  nuisance.  It  forms  a  necessary  part  of  the  Alteneder  joint, 
which  for  that  very  reason  is  not  recommended ;  it  is  a  very  good  joint,  but  not  in  any  par- 
ticular better  than  an  equally  well-made  double  one,  and  this  excrescence  makes  it  very 
objectionable  for  any  but  the  smaller  instruments,  like  those  just  described. 

15.  The  Beam-compass.— For  setting  off  distances  too  great  for  the  dividers,  and  for 
describing  circles  of  radii  beyond  the  range  of  the  ordinary  compasses,  the  instrument  shown 
in  Fig.  58  is  used. 


DRAWING  INSTRUMENTS  AND   MATERIALS.  ji 

This  consists  essentially  of  two  German  silver  sockets,  A  and  C,  which  slide  freely  on  a 
wooden  bar,  or  "beam,"  B.  The  socket  A  has  on  top  a  binding  screw,  E,  for  securing  it  at 
any  position  on  the  beam ;  the  point  of  the  screw  pressing  not  directly  against  the  wood,  but 
upon  a  metal  tongue  fixed  inside  the  socket,  which  distributes  the  pressure  and  protects  the 
beam. 

On  the  bottom  of  the  socket  is  a  cylindrical  hub,  O,  drilled  to  receive  the  shank  of  a 
plain  point,  D,  or  a  needle-point,  as  the  case  may  be,  and  fitted  with  a  binding  screw  to  hold 
the  point  in  place. 

The  other  socket,  C,  also  has  a  clamping  screw,  /,  similar  to  E,  but  on  the  lower  side 


FIG.  58 

instead  of  the  upper.  It  also  carries  a  fixed  stud,  L,  which  forms  a  bearing  for  a  journal 
turned  on  the  prolongation  of  the  screw  M,  operated  by  the  milled  head  N. 

The  nut  for  this  screw  is  the  stud  K,  fixed  on  the  socket  F,  which  is  accurately  fitted  to 
slide  on  C,  and  is  provided  below  with  a  hub,  G,  arranged  like  O  for  carrying  a  movable  point, 
a  pencil  or  a  pen.  Thus  when  C  is  clamped  to  the  beam  after  setting  the  instrument  as 
nearly  as  may  be  by  the  hand,  the  precise  adjustment  is  completed  by  turning  the  milled 
head  N. 

16.  This  is  recommended  as  the  most  convenient  form  of  beam-compass  for  general  use. 
It  will  be  noted  that  as  both  sockets  slide  on  the  beam,  it  is  easy  to  keep  the  instrument  in 
balance,  which  cannot  be  done  if,  as  in  some  forms,  one  socket  is  fixed  at  the  end  of  the  bar. 
And  also  that,  in  this  arrangement,  the  whole  adjustment  can  be  effected  without  lifting  the 
instrument  off  the  paper :  the  beam  is  naturally  supported  by  the  second  and  third  fingers  of 
each  hand,  and  without  removing  this  support,  the  screws  £,  /,  and  N  can  be  manipulated 
with  perfect  ease  by  the  thumb  and  first  finger.  Thus  with  a  two-foot  beam,  any  number  of 


PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 


circles,  varying  from  four  inches  to  four  feet  in  diameter,  can  be  drawn  without  moving  the 
needle-point  from  the  centre,  and  without  removing  the  hands  from  the  most  convenient  posi- 
tion in  handling  the  instrument. 

17.  There  are  two  arrangements  often  found  in  beam-compasses  of  different  designs, 
either  one  of  which  would  be  worse  than  the  other,  if  that  were  possible.  The  first  consists 
in  having  the  sockets  open  at  the  top,  the  binding  screws  being  placed  on  the  side ;  so  that 
they  do  not  require  a  special  beam,  but  may  be  clamped  on  any  flat  ruler ;  and  they  drop  off 
that  ruler  every  time  the  clamps  are  loosened  to  adjust  them.  The  other  consists  in  making 
the  pen  or  pencil  carrier  the  vertical  arm  of  a  bent  lever,  the  fine  adjustment  being  effected 
by  means  of  a  vertical  screw  acting  to  raise  or  lower  the  horizontal  arm  :  probably  the  worst 
adaptation  of  wrong  means  to  the  right  end  ever  contrived  by  any  human  being,  unless  the 

device  of   the  open    socket  may 
share  that  bad  pre-eminence. 

18.  The  "  furniture,"  as  it  is 
called,  of  the  beam-compass  con- 
sists of  two  plain  solid  steel 
points,  D,  D,  used  merely  in  set- 
ting off  measurements,  and  es- 
pecially useful  in  plotting  move- 
ment diagrams  on  a  large  scale ; 
a  shouldered  needle-point,  R. 
which  should  be  of  liberal  diame- 
ter in  the  body,  so  as  to  afford 
a  good  bearing  surface  ;  a  pen,  P, 
of  the  same  form  as  the  drawing 
pens ;  and  a  pencil-holder,  Q,  the 
construction  of  the  clamp  being 
like  that  before  described. 

A  beam-compass  like  that 
shown  in  the  figure,  the  sockets 
being  fitted  to  slide  easily  on  a 
satin-wood  bar  of  rectangular  sec- 
tion, five  eighths  of  an  inch  wide 
and  five  sixteenths  thick,  is  large 
enough  for  all  ordinary  work.  In 
addition  to  this,  one  of  which  the 
bar  is  three  eighths  wide  and  half 
as  thick,  with  or  without  the  slow- 
motion  screw  for  adjusting  it,  is 
an  exceedingly  convenient  thing 

FlG   5  to  have;  being  preferable  to  the 

jointed  compasses,  particularly  in 
inking  in,  when  the  circles  are  so  large  as  to  be  near  the  limit  of  the  range  of  the  latter. 

19.  Dividers  with  Tangent-screw.— This  instrument,   Fig.  59,  is  to  be  classed  among 
the  draughtsman's    luxuries.       It  is    not  very   often    wanted,    but    when    the    occasion    does 


DRAWING  INSTRUMENTS  AND   MATERIALS.  73 

come,  it  is  wanted  very  much :  as  for  instance  in  laying  out  a  wheel  whose  number  of 
teeth  is  31,  or  67,  or  any  large  prime.  There  is  in  such  cases,  as  every  expert  knows,  no 
practical  escape  from  the  operation  of  setting  the  dividers  to  the  chord,  and  "  stepping 
this  distance  off "  around  the  pitch  circle.  And  if  the  pitch  is  too  great  for  the  spacing 
divider,  Fig.  53,  the  instrument  here  shown  is  invaluable. 

It  consists  essentially  of  a  pair  of  dividers  made  much  heavier  than  the  plain  ones, 
to  one  leg  of  which  is  pivoted  the  ball  A,  so  as  to  turn  freely.  An  adjusting  screw,  C,  is 
formed  on  the  end  of  a  slotted  steel  bar,  D,  and  passes  through  the  thumb-nut  B,  which 
is  extended  into  a  journal  whose  bearing  is  in  the  ball  A  ;  "  end  shake "  is  prevented  by 
a  set-screw  with  conical  point,  which  enters  a  triangular  groove  in  the  journal.  The  other 
leg  of  the  instrument  has  a  hub  projecting  from  its  face,  upon  which  the  bar  D  rests ; 
and  into  this  hub  is  tapped  a  binding  screw,  E,  which  passes  through  the  slot.  When 
this  screw  is  loosened,  the  dividers  are  manipulated  like  the  ordinary  ones,  and  set  as 
nearly  as  possible  to  the  right  measurement ;  the  screw  E  is  then  tightened,  and  the 
adjustment  completed  by  turning  the  nut  B  in  one  direction  or  the  other  as  may  be 
required. 

20.  By  means  of   this  attachment,   the   dividers   can   not   only   be   adjusted    with   the 
utmost  accuracy  and   facility,  but  they  will   stay  so:    and   this   last  consideration  is  often 
very  important,   as  the  slightest  accident,  such   as  may  happen   to  the   most  careful  oper- 
ator, either  "  alters  the   set "  of   the   common   dividers,  or,  what   is   almost  as  bad,  leaves  it 
uncertain  whether  it  has  done  so  or  not. 

The  immense  superiority  of  this  device  to  the  common  and  cheaper  one  of  the 
"  hair-spring "  and  screw  is  too  evident  to  require  demonstration.  The  hair  dividers  are 
not  only  liable  to  accidental  derangement  through  a  movement  of  the  legs  at  the  joint, 
but  unless  the  spring  is  uncommonly  stiff,  and  the  manipulator  unusually  certain  of  hand, 
the  spacing  with  it  is  subject  to  variations  due  to  springing  of  the  adjustable  leg;  far 
more  so  than  the  small  spacing  divider,  on  account  of  the  greater  length. 

21.  As    previously   stated,   a  great    many   other   instruments    are   often    put   into   the 
larger  cases,  and  there   is  a   pleasing   delusion   that  they  make  the   outfit   more   complete. 
Among  these,  in  addition  to   the  hair   dividers,  may  be   mentioned  proportional  compasses, 
"  wholes  and  halves,"  bows  and  compasses  with  reversible  points,  "  railroad  "  or  double  pens, 
dotting  wheels,  metal   squares,  triangles  of   small  size  and   unknown   angles,  sectors,  broad 
ivory   scales  with   the   sides  covered   with   lines  and   figures  like   those  of   Gunter,    rectan- 
gular protractors,  three-legged  compasses,  three-bladed  pens,  parallel  rulers  and  opisometers. 

In  this  list  there  is  not  an  item  of  any  value  to  the  mechanical  draughtsman,  and 
hardly  one  of  practical  use  to  anybody  else ;  some  of  the  articles  are  very  expensive, 
and  none  of  them  will,  by  any  service  rendered,  pay  interest  on  the  first  cost.  Probably 
the  one  most  absurdly  overrated  is  the  proportional  compass,  which  is  a  brazen  impostor, 
and  the  use  of  it  is  a  waste  of  time. 

22.  The  Drawing1   Board.— The   best  material  for  the   drawing   board   is   clear,   well- 
seasoned,  straight-grained   white  pine,  free  from   knots   and   from   turpentine.     If  the  board 
be  too  large  to  be  made  of   a  single  piece,   the  requisite   breadth   is   made  up  of   two  or 
more  pieces  by  simply  matching  and  gluing  the  edges,  without   tongues  or  grooves. 

In  order  to  prevent  the    board   from    warping,   two  battens   of    hard  wood  are  fitted 


74 


PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 


into  dovetailed  grooves  across  the  back ;  these  should  be  fitted  accurately,  so  as  to  require 
to  be  driven  in,  but  on  no  account  should  they  be  glued  in.  The  object  is  to  allow  the 
board  tc  expand  or  contract  as  it  will,  sliding  slightly  on  the  battens,  and  no  fastening 
must  interfere  with  this  freedom.  In  order  to  weaken  the  board  transversely,  and  thus 
lessen  its  power  to  warp,  the  back  is  run  lengthwise  over  a  circular  saw,  thus  cutting  a 
series  of  slits  half  through  its  thickness,  from  a  half  to  three  quarters  of  an  inch  apart,  as 
shown  in  Fig.  60,  which  represents  a  drawing  board  such  as  above  described. 

If  the  board  be  a  large  one,  it  may  advantageously  be  not  only  weakened  but  light- 
ened by  planing  a  series  of  grooves  in  the  back,  instead  of  merely  slitting  it ;  these  may 
be  three  quarters  of  an  inch  wide,  and  the  ribs  left  between  them  of  the  same  breadth, 
making  the  section  of  the  board  appear  as  shown  at  A.  The  battens  for  large  boards  may 
also  be  more  easily  fitted  if  made  in  two  pieces,  as  at  B.  which  should  be  both  glued 


FIG.  60. 

and  screwed  together :  the  upper  strip,  which  slides  into  the  dovetail  groove,  should  always 
be  of  ash,  cherry,  or  similar  hard  wood,  but  the  lower  and  larger  piece  may  be  of  pine. 
The  ends  and  edges  of  the  drawing  board  should  be  planed  true  and  smooth,  and  its 
upper  surface  sand-papered.  But  no  oil,  paint,  varnish,  or  polish  of  any  kind  should  be 
applied  to  any  part  of  it. 

The  above  is  believed  to  be  the  best  construction  possible  for  a  board  made  entirely 
of  wood:  and  even  if  an  iron  frame  were  to  be  used,  substantially  the  same  principles 
should  be  adhered  to  in  making  the  wooden  centre.  This  is  mentioned  here,  because  it 
must  be  admitted  that  the  most  minute  precision  can  be  attained  only  by  the  use  of 
metal  straight-edges  and  squares,  including  the  edges  of  the  drawing  board  and  both  stock 
and  blade  of  the  T-square.  But  for  the  ordinary  purposes  of  the  mechanical  draughts- 
man a  sufficient  degree  of  accuracy  can  be  secured  by  using  wood  instead  of  metal. 

23.  The  T-square. — Two  forms  of  this  important  instrument  are  shown  in  Fig.  61, 
one  with  a  fixed,  the  other  with  a  movable,  blade.  In  the  first  the  blade  is  usually  se- 
cured to  the  side  of  the  stock  by  gluing,  as  well  as  by  the  screws  shown.  But,  however 
it  is  fastened,  let  it  be  noted  that  it  is  not  let  into  the  stock,  or  head,  but  simply  laid 
over  it:  thus  when  in  use,  the  upper  side  of  the  stock  is  flush  with  the  face  of  the  paper. 
This  allows  the  triangle  to  slide  past  the  edge  of  the  paper,  at  the  left,  instead  of  being 
arrested  by  the  inside  of  the  stock  as  when  the  blade  is  let  into  it. 


DRAWING  INSTRUMENTS  AND  MATERIALS. 


75 


The  same  construction  is  adhered  to  in  the  other  form,  the  blade  in  that  case  being 
held  in  any  desired  position  by  two  binding  screws.  The  inner  one  of  these  is  fixed  in 
the  stock,  and  passes  through  a  hole  in  the  blade,  thus  serving  as  the  centre  of  rotation 
when  the  milled  nut  is  loosened.  The  other  one  has  a  round  head  below  the  stock,  and 
a  portion  of  .the  neck  of  the  screw  is  fitted  to  slide  in  a  circular  slot  in  the  stock  itself, 
whose  centre  is  the  first  screw:  it  then  passes  through  another  hole  in  the  blade  and  is 
fitted  above  with  a  milled  head  like  the  other  one.  Thus  the  blade  is  easily  set  at  any 


e 


<s       s 


FIG.  61. 

angle,  and,  what  is  most  important,  it  can  be  set  firmly;  and  this  is  due  to  the  use  of  two 
screu's.  In  many  styles  of  "swivelling  heads,"  as  they  are  called,  but  one  screw  is  used,  and 
the  strength  of  a  Samson  will  not  suffice  to  fix  the  blade  with  the  requisite  firmness. 
This  forms  a  very  excellent  square :  two  correspondingly  placed  holes  for  the  screws 
should  be  made  at  the  other  end  of  the  blade,  and  all  these  four  should  be  bushed  with 
brass :  thus  the  blade  can  be  reversed  in  the  case  of  injury  to  the  upper  edge,  and  also 
detached  and  used  as  a  simple  ruler 

The  blade  should  be  made  of  wood  which  is  fine-grained  and  hard.  If  of  a  single 
piece,  probably  satin-wood  is  equal  if  not  superior  to  any  for  large  blades,  though  solid 
ebony  is  used  for  very  small  ones.  But  a  blade  of  any  size  may  be  made  with  ebony 
edges,  and  such  blades  are  the  best  of  all :  the  well-defined  contrast  between  the  paper 
and  the  ruler  materially  lessens  the  strain  on  the  eyes,  and  the  grain  of  the  ebony  itself 
is  admirably  adapted  to  the  purpose.  Such  are  the  ones  shown  in  the  figure :  the  body 
of  the  blade  may  in  this  construction  be  made  of  any  wood  that  pleases  the  fancy  ; 


76  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 

satin-wood  and  mahogany  arc  very  suitable.  The  finish  that  can  be  given  to  these,  with- 
out any  application  in  the  nature  of  varnish,  is  sufficient  for  practical  uses ;  though  the 
beauty  is  enhanced  by  "  French  polishing,"  and  also  the  liability  to  become  soiled  by 
adhering  dust  is  diminished,  and  they  are  more  readily  cleaned.  But  on  no  account 
should  any  instruments  of  wood  be  "finished  in  oil,"  as  they  sometimes  are:  which  is 
worse  than  no  finish  at  all.  Hard  rubber  is  sometimes  used  for  blades;  but  unless  for 
what  might  be  called  miniature  instruments  it  cannot  be  recommended,  being  too  flex- 
ible and  too  brittle  for  those  of  any  size. 

24.  The  dimensions  and  proportions  of  the  drawing  board  must  of  course  depend  to 
a  great  extent  upon  the  nature  of  the  work  to  be  done,  as  well  as  on  the  fancy  of  the 
user.  The  one  represented  in  Fig.  60  is  of  convenient  size  for  a  portable  article,  to  be 
placed  on  any  table  ;  it  is  40  inches  in  length,  24%  inches  wide,  and  £  inch  thick,  the  battens 
of  ash,  one  inch  wide  by  one  inch  and  a  half  deep,  placed  about  three  inches  from  the 
ends.  For  larger  work  larger  boards  must  be  used,  and  somewhat  thicker  in  proportion : 
these  are  usually  provided  with  a  permanent  stand,  which  should  be  strong  and  substan- 
tial, what  is  known  as  the  "  saw-buck  "  pattern  being  commendable  for  rigidity,  and  prefer- 
able to  the  common  substitute  of  two  separate  trestles. 

The  size  of  the  T  -  square  should  be  in  due  proportion  to  that  of  the  board,  being 
a  little  less  in  length,  that  it  may  not  overhang  and  be  liable  to  accidental  blows.  For 
such  a  board  as  the  one  mentioned  above  the  blade  should  be,  say,  34  or  36  inches  in 
length,  about  2\  inches  wide,  and  a  full  sixteenth  of  an  inch  thick.  The  head,  or  stock, 
which  is  also  faced  with  ebony,  as  wearing  better  against  the  end  of  the  board  than 
softer  woods,  should  be  about  10  inches  long,  2\  wide,  and  five  sixteenths  of  an  inch 
thick :  this  relates  of  course  to  the  plain,  not  the  swivelling,  form  of  head,  though  the 
latter  should  be  of  about  the  same  length.  For  larger  work  the  square  is  correspondingly 
larger  and  thicker:  in  which  case  the  edges  should  be  chamfered,  because  the  edge  of  any 
ruler  is  inconvenient  and  unreliable  in  use  if  much  more  than  one  sixteenth  of  an  inch 
thick,  (at  mqst  it  should  never  exceed  one  eighth,)  since  the  pencil  or  pen  must  touch  the 
upper  corner  only.  The  thickness  of  the  blade  should  always  be  such  that  it  can  be  lifted 
from  the  board  easily  by  means  of  the  stock  held  in  the  left  hand  only;  if  too  thin  for 
this,  it  is  too  weak. 

25.  Tests  of  Drawing  Board  and  T-square. — The  T-square  is  used  by  holding  the 
stock  against  either  the  left-hand  end,  or  the  lower  side,  of  the  drawing  board  ;  the  former 
position  is  for  drawing  horizontal,  the  latter  for  drawing  vertical,  lines.  When  used  in 
either  position,  all  the  lines  drawn  by  it  should  be  straight,  and  also  parallel.  The  first 
condition  requires  the  blade  of  the  T-square  to  be  straight;  the  second  requires  that  both 
the  inside  edge  of  the  stock,  and  the  end  and  edge  of  the  drawing  board,  should  be 
straight.  This  part  of  the  problem  then  consists  in  the  testing  of  straight-edges;  which 
is  done  by  taking  two  of  them,  and  applying  one  to  the  other,  observing  carefully  whether 
any  light  can  be  seen  between  them :  if  this  is  the  case  at  any  position  while  one  slides 
along  the  other,  it  is  evidence  of  a  fault.  But  even  if  it  does  not  happen,  the  question  is 
not  perfectly  settled,  because  each  may  be  faulty,  but  the  convexity  of  one  may  fit  the 
concavity  of  the  other.  Both  should  then  be  separately  tried  by  a  third :  if  no  defects 
be  thus  found,  the  presumption  is  that  all  three  are  correct. 


DRAWING  INSTRUMENTS  AND   MATERIALS.  77 

This  is  the  only  test  that  need  be  applied  to  the  T-square.  It  is  a  very  common 
superstition  that  one  with  a  fixed  head  is  worthless  if  the  stock  and  blade  be  not  ex- 
actly at  right  angles.  In  fact  this  is  of  no  consequence  whatever  except  for  the  sake 
of  appearance :  if  it  were,  the  use  of  a  movable  blade  would  be  very  circumscribed ;  and 
it  is  not  easy  to  see  what  gave  rise  to  this  false  idea.  Because  in  using  the  square, 
first  against  the  end,  then  against  the  side,  of  the  board,  the  two  sets  of  lines  thus 
drawn  should  be  perpendicular  to  each  other.  And  this  requires  simply  that  the  lower 
left-hand  corner  of  the  board  shall  be  true ;  that  is,  that  the  left  end  and  lower  side 
shall  be  at  right  angles;  though  the  corners  of  the  board  are  preferably  slightly  rounded 
off,  as  being  thus  less  liable  to  injury.  It  therefore  makes  no  difference,  if  the  board  has 
its  "working  corner"  a  true  right  angle,  whether  the  head  of  the  square  be  thus  accurate 
or  not. 

Now,  in  order  to  test  the  squareness  of  this  corner  of  the  board,  it  is  necessary  first 
to  have  a  good  T  -  square ;  with  this  draw  a  vertical  and  a  horizontal  line,  intersecting 
near  the  centre ;  describe  a  circle  about  the  intersection :  if  the  four  parts  into  which  the 
circumference  is  cut  prove  on  careful  measurement  to  be  equal,  the  corner  of  the  board 
is  square.  If  all  four  corners  are  true,  so  much  the  better;  but  the  one  mentioned  should 
be  made  so  in  every  case,  while  the  others  are  of  less  consequence. 

26.  The  Triangles,  or  Set-squares. — These  are    among   the   most    serviceable   appli- 
ances  used   in   drawing,   and    are  seldom    out  of   the  hands  of  the  expert.      They  consist 
merely  of  two   right-angled   triangles,  the  one  having   two  angles  of  45°,  the  other  having 
one  angle   of  60°  and  one  of   30°,  as  shown  in  Fig.  61.      They  are  to  be  found  in   great 
variety  of   material  and  of   style ;    some  being  made  of   a  single  piece  of  wood,  others   of 
hard   rubber,  some  of  metal,  and   they  can   be   had  of   glass.      For  ordinary  practical    use 
the  choice  lies  between  those  of  hard  rubber  and  those  of  wood,  framed  as  shown  in  the 
figure ;    those   of   a   single  piece  of   wood   are   not  at  all  to  be  relied   on,  but  the  framed 
ones  are,  if  thoroughly  seasoned.     As  in  the  case  of  the  T-square,  the  best  are  those  with 
ebony  edges,  the  main   frame  being  of  mahogany  or  satin-wood. 

A  pair  of  triangles,  or  one  triangle  and  any  straight-edge,  is  the  best  parallel  ruler 
that  can  be  found.  For  this  particular  purpose,  it  would  not  matter  what  the  actual 
angles  were ;  but  the  facility  of  drawing  short  vertical  lines  by  placing  a  triangle  against 
the  T-square  without  moving  the  latter  from  the  horizontal  position,  at  once  suggests  the 
advisability  of  having  one  angle  of  90°  in  each,  which  also  enables  the  operator  to  draw 
two  lines  perpendicular  to  each  other  through  any  point  and  in  any  position.  And  the 
frequent  recurrence  of  lines  at  angles  of  30°,  45°,  and  60°  with  the  horizontal  or  with  the 
vertical,  in  mechanical  constructions,  is  a  sufficient  reason  for  the  adoption  of  those  values 
in  the  triangles  for  common  use;  though  for  special  purposes  other  values  may  occasionally 
be  required.  The  draughtsman  should  have  one  pair  of  triangles  measuring  ten  or  twelve 
inches  on  the  longest  side;  and  another  pair  of  six  or  seven  inches  will  be  found  very 
convenient.  These  if  of  hard  rubber  will  be  about  one  sixteenth  of  an  inch  thick;  if 
framed  of  wood,  somewhat  thicker. 

27.  Tests  of  Triangles. — To   test   the    right   angle,   place   the   T-square   horizontally, 
and  draw  a  vertical  line  with   the  triangle,  placing  its  base  against  the  upper  edge  and  its 
hypothenuse   sloping   to   the   left.     Then    reverse   the    triangle,    making    the    hypothenuse 


7  8  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 

slope  to  the  right,  but  keeping  the  base  in  contact  with  the  square.  Then  a  vertical 
line  drawn  by  the  same  edge  as  before,  should  coincide  exactly  with  the  one  first  drawn. 

To  test  the  angles  of  45°,  draw  a  vertical  and  a  horizontal  line  through  the  centre 
of  a  circle  whose  radius  is  a  little  less  than  the  short  side  of  the  triangle.  Place 
the  T-square  horizontally,  its  upper  edge  a  little  below  the  centre  of  the  circle,  and 
against  this  edge  place  the  hypothenuse  of  the  triangle.  Draw  first  a  radius  by  one 
side  of  the  triangle,  sloping  one  way,  then  slide  the  instrument  along  and  draw  an- 
other radius  by  the  other  edge,  sloping  the  other  way.  Each  of  these  radii  should 
bisect  exactly  the  quadrant  which  it  cuts. 

Another  method  is  to  draw  the  circle  of  a  diameter  a  little  less  than  the  hypoth- 
enuse, divide  it  into  quadrants  by  the  vertical  and  horizontal  line  as  before ;  then 
placing  the  T-square  with  its  upper  edge  a  little  below  the  lowest  point  of  the  cir- 
cumference, place  a  short  leg  of  the  triangle  against  it,  and  draw  a  diameter  sloping 
one  way  by  the  hypothenuse.  Then  use  the  other  short  leg  as  a  base  without  turn- 
ing the  triangle  over,  and  draw  another  diameter  sloping  the  other  way :  these  two 
diameters  should  also  bisect  the  quadrants,  and  moreover  should  coincide  exactly  witli 
two  other  diameters  similarly  drawn,  but  with  the  other  surface  of  the  triangle  in 
contact  with  the  paper. 

To  test  the  angles  of  60°  and  30°,  draw  the  circle,  cut  into  quadrants  by  the 
vertical  and  horizontal  lines,  as  before ;  and,  applying  the  short  leg  of  the  triangle  to 
the  horizontal  edge  of  the  T-square,  draw  a  diameter  by  the  hypothenuse.  The  chords 
of  the  arcs  thus  determined,  measured  from  the  extremities  of  the  horizontal  diam- 
eter, should  each  be  exactly  equal  to  the  radius.  Still  keeping  the  same  surface  in 
contact  with  the  paper,  apply  the  long  leg  to  the  T-square  and  draw  another  diam- 
eter ;  the  chords  of  the  arcs  measured  from  the  extremities  of  this  diameter  to 
those  of  the  vertical  one  should  also  be  exactly  equal  to  the  radius.  And  the  same 
should  be  true  also  when  the  other  surface  of  the  triangle  is  placed  on  the  paper 
and  the  same  process  repeated. 

28.  Abstractly,  of    course,  the     short    legs     of    the    45°    triangle    ought     to    be    equal 
to    each    other,    and     the    shorter     leg   of   the   60°    triangle    should     be    one    half    the    hy- 
pothenuse ;    but     no    reliance    can    be     placed    on    a    test    depending    upon    those    proper- 
ties, for    practically   it    is    almost    impossible    to    make    the     angles    rigorously   sharp,    and 
quite    so    to     keep    them    in     that    condition;    which     is     of     no     consequence    whatever, 
since    a    line    is    never    drawn    by  either   side    quite    to    the    extremity.     But    the    inclina- 
tions   of   the    sides   to    each    other    should    be    as    exact    as    it    is    possible     to     have     them 
made;    for   then    these    little    implements,  in    connection    with    the    T-square    and    a    true- 
cornered    drawing    board,  enable  the  draughtsman   with    the   utmost   facility   to    divide    the 
circle    into    four,    six,    eight,    or    twelve    parts    as    may    be    desired,    and     to    draw    with 
equal    ease    the    inscribed     or     circumscribed     equilateral     triangle,    square,    hexagon,    and 
octagon. 

29.  Sweeps,  or   Irregular  Curves.— The    mechanical  draughtsman    frequently  has  to 
deal    with    curves    which    are    not    circular.     In    many  cases    these    can    be    made     up    of 
approximating     circular     arcs:     but     in     others     this    expedient    cannot     conveniently    be 
employed.     Even    when    it    can     ultimately    be    used    to    advantage,    it     is     often     much 


DRAWING   INSTRUMENTS  AND   MATERIALS. 


79 


better  to  draw  the  line  accurately  in  pencil  through  the  points  which  are  determined 
by  construction  according  to  the  given  law  of  the  curve,  than  to  attempt  at  once 
to  find  the  circular  arcs  which  can  be  substituted  for  it. 

For  practical  purposes,  in  general  work,  no  mechanical  contrivance  for  drawing 
curves  by  continuous  motion,  such  for  instance  as  an  elliptograph,  is  of  service  to 
an  extent  anything  like  proportionate  to  its  cost.  Such  contingencies  as  these  are 
best  provided  against  by  the  possession  of  a  selection  of  curved  rulers,  or  sweeps 
as  they  are  technically  called.  The  forms  of  these  should,  in  general,  conform  to 
some  mathematical  law,  according  to  which  the  curvature  varies  with  regularity :  and 


FIG.  62. 

the  dimensions  must  be  in  accordance  with  the  scale  of  the  work  in  hand.  For 
instance,  there  are  to  be  had  sets  of  ellipses  and  of  hyperbolas,  of  varying  eccen- 
tricities, and  parabolas  on  different  scales ;  and  these  are  in  many  cases  of  great  use. 
There  are  also  to  be  had  "  French  curves,"  "  scrolls,"  or  "  universal  curves"  without 
number  and  without  value.  In  these  last,  the  radius  of  curvature  almost  always 
changes  abruptly  at  various  points,  which  destroys  their  regularity  and  their  utility  in 
drawing  curves  not  similarly  characterized. 

In  Fig.  62  are  shown  the  contours  of  a  number  of  what  are  known  as  the 
"  Copenhagen  Ship  Curves ;"  which,  though  originally  intended  for  the  use  of  naval 
architects,  have,  with  the  addition  of  one  or  two  logarithmic  spirals,  been  found  of 
most  material  use  in  the  drawing  of  machinery:  they  are  here  reduced  to  about  one 
half  of  the  actual  size.  In  a  great  many  cases  these  are  of  use  in  inking  in  arcs  of 


So 


PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 


circles  of  a  few  degrees  only  in  length ;  especially  when  these  are  tangent  to  two 
other  lines,  as  much  time  is  saved  by  using  the  drawing  pen  thus  guided,  instead  of 
adjusting  the  inking  point  of  the  compasses,  to  say  nothing  of  the  greater  facility 
in  making  the  joinings  of  the  lines  neat  and  smooth. 

Fig.  63  shows  a  selection  of  larger  curves  from  the  same  set  as  the  others :  not 
merely  of  greater  size,  but  of  greater  radii  of  curvature,  or  in  other  words  flatter.  These 
in  particular  have  been  found  of  great  utility  in  the  laying  out  of  screw-propellers ; 
and  are  shown  on  a  scale  of  about  one  third  of  the  actual  size.  The  very  best  material 


FIG.  63. 

for  these  articles  is  hard  rubber ;  and  all  those  here  shown,  as  well  as  the  whole  set 
of  "  Copenhagen"  curves,  and  some  of  English  origin  specially  adapted  for  the  drawing 
of  the  "  lines"  of  vessels,  are  now  to  be  had  of  this  substance,  which  is  so  far  supe- 
rior to  wood  of  any  kind  as  to  be  in  the  end  much  cheaper. 

30.  The  Scale. — The  draughtsman's  scale  is  a  piece  of  metal,  wood,  or  ivory,  one 
edge  of  which  is  divided  into  inches,  and  these  again  are  subdivided  into  halves,  fourths, 
eighths,  and  sixteenths.  This  is  called  the  full-size  scale,  and  is  used  in  laying  out  draw- 
ings of  the  actual  size  of  the  objects  represented. 

The  scale  is  thus  graduated,  to  correspond  with  the  scales  and  folding  rules  used  by 
the  workman ;  this  unit  and  this  system  being  in  use  throughout  the  country.  The 
merits,  if  there  are  any,  of  the  metric  system  of  measures,  and  the  advantages,  real  or 
fancied,  of  the  decimal  system  of  subdivision,  are  foreign  to  the  question ;  what  is  used  in 
the  shop  must  be  used  in  the  drawing  office,  and  that  definitely  settles  the  matter. 

Working  drawings  are  preferably  and  usually  made  "  full  size,"  unless  they  would 
thereby  be  either  too  large  or  too  small  to  be  conveniently  worked  from.  In  that 


DRAWING  INSTRUMENTS  AND  MATERIALS.  81 

case  they  must  be  made  upon  a  smaller  or  a  larger  scale ;  that  is  to  say,  an  inch  must  be 
represented  by  a  distance  less  or  greater  than  an  actual  inch,  and  its  multiples  or  submul- 
tiples  are  of  course  reduced  or  enlarged  in  the  same  proportion  :  the  result  being  the 
same  as  if  a  full-size  drawing  were  made  of  a  smaller  or  a  larger  object. 

31.  Now,  reduced  or  enlarged  drawings  can   be   made  with    the   aid  of   only  the  scale 
above   mentioned.     If,  for  instance,  a  "  quarter-size  "  drawing  is  wanted,  each  dimension  of 
the  object  is  divided  by  four,  and   the  quotient   set   off  with   the   full-size   scale.      This, 
however,  is  not  expeditious,  by  reason  of  the  amount  of  mental  arithmetic  involved ;  it  is 
very  easy  to  divide   by  four,  but   the   operation  soon   becomes  monotonous  and  vexatious 
by  repetition.     And  this  repetition  can  be  wholly  avoided  by  the  simple  expedient  of   di- 
viding the  scale  itself  by  four  at  the  outset ;  then  with  this  contracted  scale  the  measure- 
ments of  the  actual  dimensions  are  set  off,  without  dividing  them. 

Thus,  the  quarter-size  scale  is  formed  by  taking  three  inches  to  represent  one  foot : 
this  three-inch  space  being  divided  into  twelve  equal  parts,  each  of  them  represents  one 
inch  ;  and  these  are  subdivided,  like  the  actual  inches  on  the  full-size  scale,  into  halves, 
fourths,  and  eighths. 

In  like  manner,  any  distance  may  be  selected  to  represent  a  foot,  and  a  similar 
scale  constructed  by  dividing  it  into  twelve  parts,  and  subdividing  them  as  before.  Such 
scales  are  usually  designated  by  specifically  stating  the  distance  taken  to  represent  one 
foot ;  as,  for  example,  "  3  inches  to  the  foot,"  "  i£  inches  to  the  foot,"  "  i  inch  to  the  foot," 
etc.;  which  for  brevity's  sake  are  colloquially  called  the  3-inch  scale,  the  li-inch  scale,  the 
i-inch  scale,  and  so  on. 

32.  One  of  the   most   convenient   forms  of  scales  is  shown   in   Fig.    64.      The  gradua- 
tions extend    to    the  very   edge,    and    when    the   scale    lies  upon     its    side    they    are    thus 

p;-'""*''1*''1"1'''1'1"1!  j  t 

FIG.  64. 

brought  into  direct  contact  with  the  paper,  so  that  measurements  may  be  set  off  directly, 
using  either  a  pencil  or  a  needle  as  may  be  desired.  This  is  a  very  important  feature ; 
no  work  can  be  executed  with  any  reasonable  degree  of  rapidity  if  the  measurements 
are  taken  from  the  scale,  and  set  off,  with  the  dividers  or  compasses ;  which  should  be 
done  only  in  case  of  necessity.  Again,  operations  are  much  facilitated  in  many  cases  by 
laying  the  scale  against  the  upper  edge  of  the  T-square,  and  thus  pushing  it  along  until 
the  edge  reaches  the  line  along  which  distances  are  to  be  set  off :  and  the  triangular  scale 
lends  itself  readily  to  this  mode  of  using  it. 

The  peculiar  formation  of  this  instrument  allows  a  number  of  different  scales  to  be 
cut  upon  its  various  edges.  This,  to  be  sure,  is  not  an  unmixed  advantage,  as  among  so 
many  it  is  not  always  easy  on  the  instant  to  find  the  one  wanted,  and  were  it  not  for 
the  bulk  and  the  expense,  it  would  perhaps  be  more  convenient  in  many  instances  to 
have  but  one  or  two  scales,  upon  one  edge  only.  This  would  necessitate  the  use  of  a 
number  of  separate  instruments,  and  the  inconvenience  thus  caused,  as  well  as  the  in- 
creased expense  of  material,  prevent  these  separate  scales  from  being  placed  on  the  mar- 
ket in  any  form  more  substantial  than  that  of  printed  strips  of  paper.  These  are 


82  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 

not  very  durable,  but  they  possess  one  commendable  feature,  that  of  expanding  and  con- 
tracting as  the  moisture  of  the  air  varies,  pretty  nearly  in  the  same  ratio  as  the  paper 
upon  which  the  drawing  is  made. 

33.  These    triangular  scales  are    made  both  of   metal  and   of  wood.      The   former   are 
not  solid,  but    made  of  drawn  brass  tubing,  with  closed  ends,  nickelled   with    a  dull    finish. 
They   are  thus   very   light,    and    possess   the    advantages   of   not    being   liable    to    warp,    or 
crack,    or   chip   at   the   edges ;    nor   are    they  subject    to    variations   due    to   moisture  like 
those  of  wood.       On  the  other  hand,  they  are  more  trying  to    the  eyes,    the  graduations 
not  being  so  strongly  in   contrast   with  the  surface ;  and   thus  far  they  are  not  to  be    had 
over  one  foot  long. 

This  is  long  enough  for  some  purposes,  of  course ;  but  in  general  practice  in  machine 
drawing,  there  are  so  many  measurements  of  more  than  one  foot  to  be  laid  off,  that  a 
longer  one  is  almost  a  necessity,  if  facility  and  speed  are  of  account. 

Those  of  boxwood  are  to  be  had  both  18  and  24  inches  in  length:  of  these  the 
former  is  more  convenient  under  average  circumstances.  It  is,  besides,  of  considerably  less 
first  cost,  and  it  is  much  easier  to  find  a  perfect  one ;  and  when  good  at  the  beginning, 
it  is  more  likely  to  remain  good  ;  for  the  difficulty  of  finding  a  piece  of  wood  which  will 
not  check  or  warp  sooner  or  later,  increases  very  rapidly  with  the  length. 

34.  The  edges  of  these  instruments  are  usually  divided  to  scales  of  T3^,  -fa,  £,  £,  |,  |,  J, 
I,  i^,  and    3  inches  to  the  foot,  and  the  remaining  edge  has  the  full-size  scale  above  men- 
tioned :    some  have  a  4-inch  and  a  2-inch    scale    upon  one    edge,  instead  of  the  T3^  and  -fa 
scales ;   but  neither  one  of  these  four  is  very  frequently  made  use  of. 

In  selecting,  the  purchaser  should  see  that  the  wood  is  free  from  veins  or  streaks,  be 
careful  to  note  that  it  is  as  nearly  straight  as  possible  (absolute  perfection  in  this  respect 
is  hardly  to  be  expected  of  wood),  and  above  all  things  that  the  graduations  are  fine  and 
clean-cut.  This  last  they  are  almost  sure  to  be  if  the  maker  be  one  of  reputation,  and 
there  are  those  whose  names  are  of  themselves  a  guarantee  of  accuracy ;  but,  on  the  other 
hand,  scales  of  this  popular  form  are  to  be  found  upon  which  the  lines  are  very  coarsely 
cut :  this  is  a  fatal  defect,  and  all  such  should  be  rejected,  no  matter  how  good  they  may 
be  in  other  particulars ;  the  mere  fact  of  being  stamped  "  U.  S.  Standard  "  is  not  alone 
sufficient,  but  the  graduations  of  the  smallest  scales,  such  as  the  T3T,  -fa,  %,  and  \,  should 
bear  close  scrutiny  with  a  magnifying  glass  without  revealing  irregularity  of  divisions  or 
blurring  of  lines. 

MATERIALS  AND  MISCELLANEOUS  ARTICLES. 

35.  Drawing  Paper. — In  order  to  do  good  work,  the  draughtsman  should  be  provided 
with  good  materials  as  well  as  good  instruments.     For  fine  work   in   ink,  Whatman's   hot- 
pressed    paper    is    no  doubt  superior  to  any  other,    for    making   both    detail    and   general 
drawings  of  machinery. 

It  is  to  be  noted  that  the  thickness  of  this  paper  varies  with  the  size  of  the  sheet ; 
and  the  size  known  as  "  double  elephant  "  (27  by  40  inches)  has  a  body  and  substance 
peculiarly  well  adapted  for  these  purposes.  It  may  also  be  stated  that  this  is  as  large  a 
sheet  as  ought  to  be  used,  unless  for  very  particular  reasons.  Anything  larger  than  this 
is  inconvenient  to  handle  as  a  working  drawing  in  the  shop  ;  and  with  a  judicious  se- 


DRAWING  INSTRUMENTS  AND   MATERIALS.  83 

lection  of  the  scales,  it  is  large  enough  for  the  details  of  the  most  massive  machinery. 
Occasions  will  arise,  as  in  making  plans  of  vessels,  etc.,  in  which  these  dimensions  must 
be  exceeded ;  but  it  is  usually  in  length  only,  a  wider  drawing  being  seldom  called 
for. 

Where  4rawings  are  to  be  at  once  sent  into  the  shop  and  worked  from,  without 
tracing,  a  cheaper  paper  may  be  desired.  In  this  case  the  article  known  as  "  Duplex " 
paper,  a  Manila  paper  of  a  fine  creamy  tint,  serves  an  excellent  purpose.  It  takes  ink 
fairly  well,  and  for  drawing  in  pencil  only,  is  better  than  Whatman's ;  it  is  to  be  had  of 
a  size  very  nearly  the  same  as  the  double  elephant. 

36.  But   of   whatever  make    or   quality,  the    paper   should    be  procured  in   sheets,  and 
kept  flat,  if  it  is  expected  to  do  even  tolerable  work. 

With  a  mistaken  idea  of  economy,  paper  is  sometimes  procured  in  huge  rolls,  and 
cut  off  as  required.  If  every  piece  is  "  damp -stretched  "  before  using,  this  may  answer; 
but  that  costs  more  in  time  than  is  saved  in  the  purchase.  If,  on  the  other  hand,  it  is 
merely  pinned  down  as  usual,  no  one  can  draw  upon  it  as  well  or  as  rapidly  as  he  can 
upon  a  flat  sheet  lying  smoothly  on  the  board. 

The  best  course  is  to  procure  a  considerable  quantity  at  a  time ;  if  it  must  be  rolled 
for  transportation,  let  the  roll  be  as  large  as  possible,  and  as  soon  as  may  be,  put  the 
whole  into  a  drawer  of  suitable  size,  that  the  weight  may  act  to  make  it  flat  again  and 
keep  it  so.  The  larger  the  stock  laid  in,  the  better;  for  whatever  the  reason  may  be,  good 
paper  improves  by  age. 

37.  It   seems   not  to   be  as  generally  known  as  it  might  be,    that    for   many  purposes 
common  writing  paper  is  admirably  adapted.     Not,  to    be   sure,  for  making  working  draw- 
ings ;    but    for    fine   diagrams,    and    for  illustrative  drawings,    it  is  perhaps  better  than  any 
other.     The  best  is  the  heaviest  linen  "  ledger "  paper,  which    has  not  only  a  surface  upon 
which  the   finest    ink  lines    can    be  drawn,    but    sufficient    body  to    permit    erasures    to    be 
made,  still  leaving  the  paper  in  condition  to  take  the  ink  without  spreading.     And  thinner 
writing  papers  answer  exceedingly  well  for  making  tracings. 

38.  Pencils. — It  is    universally  conceded    that   in  all    the  essential    qualities  of   a  good 
drawing  pencil,  those  made    by  Faber  are    unsurpassed.       They  are  to  be  had  of   different 
degrees  of  excellence  as  well  as  of  hardness ;  the  "  Siberian"   are  the  best.     Those  marked 
HHHH    are,  as  regards    hardness,  most    suitable  for  general  use,  as  if  softer,  they  do  not 
make  a  fine  enough  line  nor   keep  long  enough    in  good  trim,  and  if  harder,  the  lines  are 
not  so  easily  erased   as   is  desirable.     But  for  making  the  very  finest  work,  where  there  is 
reasonable    certainty    that    little    if   any   erasing  will    be    necessary,    the    HHHHHH   grade 
may  be  used  to  good  advantage. 

And  this  last  grade  should  always  be  the  one  chosen  for  the  "  instrument  leads," 
already  mentioned  in  connection  with  the  compasses  and  pencil  bows :  as  there  is,  appar- 
ently, a  difference  between  the  gradings  of  these  leads  and  of  those  used  in  the  pencils, 
and  these  will  be  found  none  too  hard. 

39.  Rubber,  Ink  Eraser,  etc. — The    rubber     for   erasing    pencil     marks    should    effect 
that  object  without  soiling  the  paper :  which  neither  the  pure   gum  (or  virgin  rubber)  nor 
the  black  rubber  will  do.     Neither  ought  the  rubber  itself  to  become  soiled  in  the  opera- 
tion ;    the   best    is     that    known    as     "  velvet "    rubber,    which   has    some   substance    incor- 


84  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 

porated  with  it  of  such  nature  that  the  whole  wears  off  quite  rapidly  in  use,  the  acting 
surface  remaining  clean  and  fresh. 

For  erasing  ink  lines,  Faber's  "  ink  eraser  "  is  the  best  article  to  use.  The  use  of  a 
knife  or  other  steel  instrument  should  be  sparingly  indulged  in ;  the  edge  should  be  very 
keen,  and  the  convex  portion  only  should  be  applied  to  the  paper,  so  as  to  scrape  its 
surface,  and  that  very  lightly:  the  use  of  the  point  of  a  knife  to  scratch  out  a  line  is  a 
barbarism.  The  ink  eraser  recommended  is  similar  to  the  velvet  rubber,  with  a  larger  ad- 
mixture of  pumice  stone,  which,  used  without  sufficient  force  or  speed  to  heat  the  paper, 
removes  the  ink  and  polishes  the  surface :  which  if  then  rubbed  lightly  with  an  ivory 
paper  folder,  will  be  in  good  condition  to  receive  ink  again.  Thus  with  due  care,  cor- 
rections and  alterations  can  be  made  so  neatly  as  to  escape  any  but  the  closest  scru- 
tiny. 

For  removing  light  marks  of  the  pencil,  and  for  cleaning  the  paper  if  dusty  or  other- 
wise soiled,  a  very  useful  article  is  now  furnished,  called  rubber  sponge.  It  is  most 
excellent  when  new,  but  in  some  way  hardens,  and  gradually  becomes  useless,  with  age. 
Equally  good  for  the  same  purpose  is  the  crumb  of  stale  wheat  bread ;  it  should  be 
broken  into  small  bits  and  well  rubbed,  or  rolled,  into  the  surface  of  the  paper,  thus 
forming  numberless  little  pellets,  to  which  the  dust  adheres. 

40.  Ink. — Ordinary  writing  ink  is  wholly  unsuitable  for  mechanical  drawing ;  it  rapidly 
corrodes  the  pens,   and   acts   chemically   upon  the  paper,  making  neat  erasure  almost    im- 
possible.      For  this    purpose,  then,   India  ink  alone   is  used  ;    it   consists  wholly  of    carbon 
and  some  adhesive  substance,  so  that   it  merely  lies  on  the  surface   of  the  paper  without 
"  biting  in." 

The  best  is  of  Chinese  manufacture,  and  comes  in  sticks  or  cakes  of  various  sizes  and 
forms ;  this  is  to  be  simply  rubbed  up  with  water  to  any  desired  density.  This  labor 
of  preparation,  slight  as  it  is,  is  to  some  persons  a  great  bugbear ;  and  in  response  to 
their  demands  various  "liquid  India  inks"  are  offered  for  sale;  the  bottles,  when  prop- 
erly cleaned,  are  good  :  which  is  more  than  can  be  said  of  the  contents. 

The  Chinese  inks  vary  greatly  in  quality  and  in  price  ;  but  it  does  not  always  hap- 
pen that  the  most  expensive  is  the  best.  That  for  line  drawings  should  be  comparatively 
soft,  while  that  to  be  used  for  tinting  with  the  brush  should  be  quite  hard  ;  but  both 
must  be  free  from  grit.  In  selecting,  wet  the  end  of  the  finger,  and  rub  the  ink  upon 
it  ;  that  for  line  work  only  should  in  a  very  few  seconds  produce  a  dense  black  spot, 
and  without  any  rough  or  gritty  feeling ;  when  dry  the  spot  should  have  a  brilliant 
lustre,  and  a  dull  or  cloudy  appearance  should  cause  it  to  be  rejected.  It  may  also  be 
noted  that  the  better  grades  of  this  ink  have,  when  wet,  an  odor  of  musk. 

Further,  the  ink  should  be  tested  as  to  its  adhesive  power.  Draw  a  broad  black 
line  with  it,  wait  until  perfectly  dry,  then  apply  the  rubber  vigorously,  as  if  erasing  pen- 
cil marks.  The  brilliance  of  the  line  may  be  impaired,  but  it  should  remain  black  and 
continuous;  if  it  does  not,  the  ink  lacks  adhesiveness,  and  is  not  suited  for  the  purpose. 

41.  The   preceding   relates  to    black  ink,  which  forms  a  perfect  emulsion,  and   deposits 
no  sediment,  merely  becoming  more  viscid   as  it  evaporates.     There  are  also  Chinese  inks 
of   different    colors,    but    they  cannot    be  recommended,    as    the    coloring    matters,    though 
very  brilliant,  are  also  very  heavy,  and   do  not  remain  well  in  suspension,     It  is  therefore 


DRAWING  INSTRUMENTS  AND  MATERIALS.  85 

quite  difficult  to  keep  the  same  tone  or  shade  in  drawing  a  number  of  lines  consecu- 
tively. For  making  lines  in  color,  then,  the  draughtsman  cannot  do  better  than  to  use 
the  cakes  of  water  colors  furnished  for  artists.  Preference  should  be  given  to  those 
which  are  most  soluble,  such  as  Prussian  Blue,  Carmine,  Scarlet  Lake,  Indian  Yellow, 
etc.:  they  are  used  exactly  like  the  India  ink ;  and  like  it  are  not  corrosive,  which  all 
the  colored  writing  fluids  are,  and  they  should  not  be  used  with  instruments  of  any 
value. 

42.  In  preparing  the  ink  for  tinting  with  the  brush,  the  stick  should  never  be  dipped 
into  the  water,   but  merely  rubbed   upon  the  wetted  finger,    which   again    is  rubbed  upon 
the  bottom  of   the  saucer  of   water.      This  is  for  the  purpose  of  preventing  any  speck   or 
flake  of  the  solid  ink,  which  is  quite  friable,  from  eventually  lodging  in  the  brush.     It  also 
serves  a  good   purpose  in  avoiding   the  immersion    of   the   stick   of    ink,   which    becoming 
soaked    and    soft,    is    still    more    apt    to  crack    and    scale  off.      And    there    is    no  doubt 
that     even     for     line    work,    the    above     is     the     best   process.       But      it      is     undeniably 
tedious ;    and    it    is  not  absolutely    necessary    to  the  execution    of    even    the   finest    work. 
For    this    purpose    it     is    admissible    to    rub    the    ink     directly    in    the    water ;     but    the 
solution,  or    emulsion,    should    afterward    be    carefully    rubbed  with    the  finger   until    it  is 
certain  that  there   are  no    bits   of  solid   ink  remaining,  for  if  one   of  these  gets   into   the 
pen,   as    it    is    tolerably  sure    to    do.   it  will    be  found  that  no  time  has  been  gained  by 
neglecting    the    precaution    here    insisted    on.      And    dust    is  nearly  as   bad ;    so    that    the 
saucer  should  be  kept  covered  after  the  ink  is  mixed  :    the  saucers  which  come  in  nests, 
each  being  a  cover    to   the   one   below,   are   very  convenient,   as   are   also  those  provided 
with  glass  plate  covers. 

Neither  the  India  ink  nor  the  colors  should  be  wetted  more  than  absolutely  neces- 
sary in  mixing,  and  they  should  be  wiped  dry  with  soft  paper,  at  once,  to  prevent  the 
absorption  of  water,  which  tends  to  disintegrate  them. 

The  blades  of  the  drawing  pen  being  moistened  by  breathing  between  them,  the  ink 
is  introduced  by  means  of  a  common  steel  writing  pen  which  has  not  been  used  with 
any  writing  fluid,  and  should  be  kept  for  this  purpose  exclusively. 

The  ink  will  look  black  in  the  saucer,  when  in  fact  it  is  not  as  dense  as  it  should 
be.  The  test  is  to  draw  a  broad  black  line  with  one  stroke  of  the  drawing  pen :  this 
when  dry  should  be  absolutely  black ;  if  it  be  grayish  or  brownish,  the  ink  is  not  thick 
enough.  It  will  of  course  become  thicker  by  evaporation  as  the  work  progresses  ;  hence 
care  should  be  taken  to  prepare  a  comparatively  large  quantity  at  the  outset :  in  dilut- 
ing it  afterward  if  necessary,  water  should  be  added  a  few  drops  at  a  time,  and  the  whole 
rubbed  with  the  finger  after  each  addition.  And  the  same  process  should  be  adopted  in 
again  mixing  ink  which  has  dried  in  the  saucer  when  set  aside,  which  is  perfectly  good 
for  line  work ;  but  for  tinting  the  saucer  should  be  washed  out  and  fresh  ink  pre- 
pared. 

43.  Drawing  Pins,  or    Thumb-tacks. — For    all    ordinary    purposes,    particularly    for 
working  drawings,  the  paper  should  merely  be  secured  to  the  board  by  a  "  drawing-pin  "  at 
each  corner,  as   shown    in   Fig.   60 :  being   placed  as  near  to  the  lower  left-hand   corner   as 
possible.     As  a  matter  of  course,  the  paper  will  expand  and   contract  to   some  extent  on 
account   of  variations  in  the  moisture   of  the  air:  for  which  an  allowance  dictated   by  ex- 


86  PRACTICAL   HINTS  FOR   DRAUGHTSMEN. 

perience  must  be  made  in  using  the  scale,  unless  the  latter  itself  be  of  paper.  But  the 
errors  due  to  this  cause  are  less  than  those  which  arise  when  a  "  stretched "  sheet  is  cut 
loose  ;  upon  which  the  paper  contracts,  and  that  not  only  to  a  variable  and  uncertain  ex- 
tent, but  not  always  evenly ;  so  that  lines  which  ought  to  be  straight  are  sometimes  quite 
the  reverse. 

The  form  of  these  drawing  pins  is  shown  in  Fig.  60:  the  heads  are  slightly  convex, 
not  bevelled,  and  the  pins  are  cylindrical  with  tapered  points ;  and  not  wholly  conical. 
They  are  so  inexpensive  that  none  but  the  best  should  be  used ;  these  are  made  by 
screwing  a  steel  pin  into  a  German-silver  head :  cheaper  ones  have  the  pin  riveted  into 
the  head,  and  the  riveting  if  slight  may  yield  under  the  pressure  of  the  thumb,  causing 
serious  injury. 

44.  Damp-stretching. — For  making  line  -  drawings  in  the  nature  of  pictures,  it  is 
sometimes  desirable  to  have  the  sheet  stretched,  as  it  undoubtedly  gives  a  smoother 
surface  than  can  be  obtained  in  any  other  way  ;  and  for  .tinting,  if  the  surface  be  of  any 
size,  it  is  indispensable.  The  operation  of  "  damp-stretching  "  consists  essentially  in  wet- 
ting the  back  of  the  paper  and  gluing  or  pasting  down  the  edges  while  thus  expanded ; 
but  to  do  this  neatly  requires  some  little  care  and  skill  :  attention  to  the  following  di- 
rections will,  however,  be  likely  to  ensure  success. 

1.  Chamfer  the  edges.     To  do  this,  lay  the  sheet,  face  up,   on  the  board,  and  with  a 
ruler  and  a  very   sharp   knife,   cut  just    through    the  surface,  about  a  quarter  of   an   inch 
from  each  edge.      The  strips  thus    partially  severed    are   now    to    be  torn  off,  taking  care 
to  pull  downward  and    away  from    the  sheet.      Thus    the  edges  will    be    left   sharp,   thin, 
and  at   the  back  slightly  roughened,  which   will   cause  the   paste  to  hold   better. 

2.  The  paper  still  lying   face  up,   fold    over  each    edge,   say  three   eighths  of  an   inch 
for  a   double    elephant   sheet,    and    for   different    sizes    in    proportion. 

3.  Turn  the   paper  face  downward,  and  wet  the  back    thoroughly,  leaving    the  folded 
edges   dry.       Water   may   be   poured    on    the  middle  of   the  sheet,  but  toward  the  corners 
the  sponge  must  be  used,  in  order  to   have  all    parts  equally    wet.         Allow    the    paper   to 
soak    until     the    whole    is    perfectly    limp ;     then    take    off    the    surface    water    with     the 
sponge. 

4.  Turn  the  paper  again  face   upward,  lay  a  sheet  of  thin   soft  wrapping    paper  upon 
it,  and    rub  with    an    old    linen    handkerchief  from   the   centre   outward,    with    considerable 
force,    to  press   out     the    wrinkles.       Lay   strips    of    paper  an  inch  wide    under  the    folded 
edges,  to    prevent    accidental    smearing   of   paste    upon    the    face    of   the   sheet. 

5.  The  best   adhesive  preparation  is  dextrine ,"  mixed  up  with  water,  not  into  a  liquid, 
but    into    a   thick  glutinous    mass;    with  which    the    edges  are  to    be  well  covered.       If    it 
should     happen    to    become    too    dry   in  any  part    before   the    edge    is    turned     down  and 
secured,    it  is   only   necessary    to  wet   it   slightly ;  and  after  the  paper  is  cut  loose,  the  re- 
maining edges  can   be  readily  removed   and  the  board  cleaned,   by  liberal  sponging. 

6.  Apply  the  dextrine   first    to  only  about   one    third    the  length   of  the  sheet,   in  the 
middle  of  one  side.     Turn  down  that  portion,  lay  a   strip    of    clean  paper  over  it,  and  rub 
hard  with  an  ivory  paper  folder  or  something  similar ;  it  is  well    also   to  put  a  thumb-tack 
at  each  end  of  the  part  thus  treated.      Then  proceed  in  like  manner  with  the  middle  part 
of  tlic  opposite  side :    take  next    the  middle  of  one    end,  then    the   part    opposite    to  that ; 


DRAWING  INSTRUMENTS  AND  MATERIALS.  87 

and  leave  the  corners   to  the    last,  completing   them    in  any  order  that  is   most    conven- 
ient. 

7.  In  removing  a  stretched  sheet  from  the  board,  cut  first  one  side,  and  next  one 
end.  If  two  opposite  sides  or  ends  are  cut  in  succession,  the  sheet  is  very  likely  to  have 
a  corner  tonv  off  by  the  contraction  of  the  paper  when  the  first  transverse  cut  is  made. 

45.  Mounted   Paper. — It   is  rarely   that  mechanical  drawings   are  subjected    to  usage- 
requiring  them  to  be  "  mounted  "  on  linen,  as  maps  frequently  are.     But  no  map  or  draw- 
ing should  be  mounted  on  linen  after  it    is  made ;   for  that  operation    involves   a   second 
wetting,    with   a  nearly   absolute   certainty   of    distortion    upon    drying.      Ready-mounted 
paper  should   be  used ;  this  may  be  stretched   as  above  explained,  that  is  by  dampening, 
and   then  fixing  the  edges  to  the  board.      But   let  it  be  observed,  that   in  this   case   the 

face  must  be  wetted,  as  the  application  of  water  to  the  back  would  loosen  the  linen  and 
ruin  the  sheet ;  also  that,  owing  to  the  weight  of  the  material,  glue  should  be  used  instead 
of  dextrine.  If  the  greatest  accuracy  in  the  finished  work  is  required,  the  sheet  should 
be  stretched  only  for  the  purpose  of  making  it  smooth,  and  it  then  should  be  cut  loose, 
and  merely  fastened  with  large  thumb-tacks  while  the  drawing  is  in  progress. 

46.  Tracing  Cloth.— This  is  used    for  making  copies  of  drawings  which  may  be  em- 
ployed either  to  work  from  directly,  or  for   reproducing  the  original   by  the  "  blue-print " 
or  other  heliographic  process.      In  the    latter  case  all  the    lines  should    be  black ;   in  the 
former,  colors  may  be  used  for  centre  lines   and  to  distinguish  one  material  from  another. 
A  good  coat  of  clear  shellac  varnish  should  be  applied  before  the  tracing  is  sent  into  the 
shop. 

In  selection,  Hobson's  choice  is  substantially  that  now  offered  the  purchaser ;  the 
manufacture  being  apparently  a  monopoly,  the  result  being  the  production  of  but  one 
quality,  which  might  perhaps  be  called  good  were  it  not  immeasurably  inferior  to  that 
formerly  furnished ;  an  article  fifty  per  cent  better,  though  no  higher  in  price,  than  any 
now  to  be  had. 

By  reason  of  this  depreciation,  there  is  great  liability  to  the  mishap  of  having  the 
ink  strike  through  the  coating  and  spread  in  the  meshes  of  the  cloth ;  the  ink  must  be 
pretty  thick,  the  pen  in  good  condition  and  lightly  used ;  but  no  precaution  will  ensure 
the  operator  against  this  most  annoying  accident,  which  never  ought  to  occur. 

47.  Tracing   Paper.— Of    this   article    there   are    fortunately   several   varieties   to   be 
found,  and  most  of  them  of  excellent  quality ;  it  is  to  be  had  in  sheets  of  various  sizes, 
and   also  in  rolls.     And  it  is  to  be  said  that  its  perfect  flexibility  prevents  any  injurious 
effect  from  keeping  it  rolled,  even  on  a  small  roller ;   when  spread  over  the  drawing  it  will 
lie  flat,  without  curling. 

Some  of  the  tracing  papers  are  white,  others  of  a  yellow  tint ;  so  far  as  the  qual- 
ity, and  the  ease  of  drawing  upon  them,  are  concerned,  there  seems  to  be  little  dif- 
ference ;  but  the  former  are  to  be  preferred  if  it  be  intended  to  make  blue-prints. 

Among  the  best  and  strongest  of  these  varieties  are  those  known  as  "  parchment 
tracing-paper,"  and  "parchment  process  tracing-paper;"  the  latter  is  remarkably  heavy 
and  tough,  the  former  thinner  but  of  similar  toughness,  and  both  are  exceedingly 
smooth  and  fine  in  surface.  There  is,  however,  one  variety,  known  as  "  vegetable 
parchment,"  against  which  the  purchaser  should  be  warned.  It  is  unusually  clear, — so 


88  PRACTICAL  HINTS  FOR  DRAUGHTSMEN. 

clear  indeed  that  it  is  not  easy  to  tell  which  lines  have  been  traced  and  which  have 
not ;  but  it  does  not  take  ink  perfectly,  and  it  expands  and  contracts  so  much  with 
apparently  no  provocation  at  all,  that  it  is  next  to  impossible  to  make  a  tracing  which 
tallies  with  the  original. 

As  before  mentioned,  some  of  the  thin  writing  papers  are  excellent  for  making  small 
tracings.  And  what  is  known  as  "bond  paper"  can  also  be  used  to  good  advantage,  if 
the  lines  of  the  original  are  not  too  fine — it  is  not  so  transparent  as  the  regular  tracing 
papers,  but  is  much  stronger  and  more  durable. 

ON    THE   USE    AND  CARE  OF   INSTRUMENTS. 

48.  The  Compasses. — In  striking  a  circle  with  a  pair  of  compasses,  the  uninstructed 
novice  is  very  apt  to  take  hold  of  the  instruments  by  the  legs,  thinking  that  they  are 
thus  more  securely  held.  This  habit  once  formed  is  difficult  to  abandon,  like  other  bad 
habits ;  at  the  very  beginning,  therefore,  the  tyro  should  accustom  himself  to  the  correct 
manipulation,  and  to  handle  the  compasses  by  the  joint  alone,  using  only  the  thumb  and 
the  first  two  fingers. 

Begin  the  circle  at  the  lowest  point,  holding  the  joint  of  the  compasses  between  the 
thumb  and  the  middle  finger,  the  index  finger  resting  lightly  against  the  left  side  of  the 
joint.  Turn  the  compasses  ivitli  the  clock,  describing  the  left  half  of  the  circumference  by 
rolling  the  joint  between  the  thumb  and  second  finger ;  that  finger  can  go  no  farther,  but 
its  place  is  then  easily  and  naturally  taken  by  the  first  finger,  and  the  joint  is  rolled  be- 
tween it  and  the  thumb  until  the  circle  is  completed,  by  one  continuous  motion.  This 
requires  a  little  practice,  but  the  trick  of  it  once  acquired  is  never  forgotten,  and  the  in- 
strument is  at  all  times  under  perfect  control,  with  no  danger  of  altering  the  radius. 
The  action  will  be  readily  understood  by  the  aid  of  Figs.  65  and  66.  In  setting  the 
compasses  to  draw  a  circle  of  given  diameter,  it  is  not  enough  simply  to  open  the  legs 
to  the  required  radius,  for  it  seldom  happens  that  this  can  be  done  with  exactness ; 
two  short  arcs  should  be  struck,  on  opposite  sides  of  the  centre,  and  the  scale  applied 
to  see  that  the  diameter  is  correct :  this  should  not  be  done  on  the  drawing,  but  on  a 
separate  piece  of  paper. 

In  order  to  make  a  line  of  uniform  thickness,  the  pen  must  be  used  with  uniform 
pressure ;  and  this  should  be  the  lightest  practicable.  If  the  pen  is  new,  that  is,  just 
sharpened,  the  merest  touch  is  sufficient,  so  that  instead  of  bearing  down,  the  operator 
should  rather  support  part  of  the  weight  of  the  compasses. 

The  fact  that  a  variation  in  the  pressure  makes  a  difference  in  the  breadth  of  the 
mark  with  either  pencil  or  pen,  is  made  use  of  in  putting  in  shadow  lines.  The  mark- 
ing point  is  put  in  motion  before  touching  the  paper,  the  pressure  gradually  increased 
towards  the  part  where  the  greatest  thickness  of  line  is  required,  then  gradually  dimin- 
ished, and  taken  off  the  paper  while  still  in  motion ;  the  whole  action  being  analogous 
to  the  use  of  a  writing  pen  in  shading  letters  and  flourishes. 

The  two  legs  of  the  compasses  should  always  be  kept  in  a  vertical  plane,  and  the 
marking  point  as  well  as  the  needle-point,  perpendicular  to  the  paper. 

Some   draughtsmen  have  a  vicious   way  of   holding  the   compasses   so  that   both  legs 


DRAWING   INSTRUMENTS  AND  MATERIALS. 


89 


lean   over,  in  the  direction  in  which  they  are   moving:    an  excellent   way  to   ream  out   a 
conical  hole  at  the  centre  of  the  circle,  and  to  spoil  the  pen  at  the  same  time. 

94.  The  Dividers. — These   should  be  handled  in  the  same  manner  as  the  compasses ; 


FIG.  65. 

that  is  to  say,  they  should  be  held  by  the  joint  only,  and  not  by  the  legs;  which  last  is 
not  only  awkward  to  a  degree,  but  is  very  liable  to  derange  the  adjustment.  In  "  step- 
ping off"  a  measurement  repeatedly  along  a  line,  or  around  a  circle,  they  should  not  be 


' 


FIG.  66. 


lifted  entirely  off  the  paper,  but  first  one  point  and  then  the  other  is  taken  as  a  centre, 
and  the  instrument  is  manipulated  as  if  describing  a  series  of  semicircles,  the  rotations 
being  alternately  with  and  against  the  clock.  Thus  it  is  never  required  to  shift  the  di- 


90  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 

viders  in  the  hand,  which  would  be  unavoidable  were  the  attempt  made  to  turn  them 
over  and  over  in  the  same  direction.  And  the  same  is  true  in  handling  the  spacing  di- 
vider, which  is  the  only  one  of  the  bow  instruments  requiring  mention  here. 

50.  The  Drawing  Pen. — This  is  held  by  the  thumb  and  first  two  fingers ;  the  third 
and  fourth  fingers  resting  lightly  on  the  ruler,  steady  the  hand  and  control  the  pressure, 
or  at  least  aid  in  keeping  it  uniform,  which  is  necessary  in  order  to  draw  an  even 
line.  It  has  already  been  stated  that  if  properly  set,  the  pen  will  do  its  best  work 
when  held  upright ;  as  in  Fig.  67.  If  it  be  not,  then  it  may  be  necessary  to  incline 
it  slightly,  the  top  being  a  little  in  advance ;  but  this  should  be  avoided  if  possible. 

It  is  sometimes  desired  to  draw  a  very  broad  line,  as  for  instance  in  making 
a  border  around  a  picture.  In  such  a  case  the  attempt  should  not  be  made  to  cover 
the  whole  stripe  with  ink  at  once ;  but,  ruling  a  series  of  parallel  lines  close  together, 


FIG.  67. 

each  as  thick    as    the    pen    will    draw    conveniently,  wait    till    these    are  perfectly  dry,  and 
then  draw  another  series  overlapping  them  and  thus    filling  in    the  spaces. 

It  is  imperatively  necessary  to  keep  the  blades  of  all  the  pens  clean  both  inside 
and  out,  if  the  best  results  are  to  be  attained.  While  using  them,  the  ink  should 
never  be  allowed  to  become  too  thick;  at  the  first  sign  of  this,  pass  a  strip  of  paper, 
folded  once  or  twice,  between  the  blades,  and  refill  the  pen.  And  the  ink  should  not 
be  allowed  to  dry  in  the  pen  under  any  circumstances ;  on  laying  one  down,  even  for 
a  short  time,  it  should  be  cleaned.  For  this  purpose,  a  bit  of  paper,  folded  so  as 
to  require  some  pressure  to  pass  it  between  the  blades  from  screw  to  tip,  answers  best ; 
the  blades  will  spring  apart,  but  their  elasticity  keeps  the  paper  in  contact  with  the 
inner  surfaces.  This  should  be  repeated  until  no  more  ink  is  seen  on  the  paper  even 
if  it  be  moistened. 


DRAWING   INSTRUMENTS  AND  MATERIALS.  91 

Neglect  of  this  is  the  real  cause  of  much  bad  work  for  which  the  pen  is  wrong- 
fully blamed ;  it  is  unreasonable  to  expect  a  blade  thickly  encrusted  with  ink  to  make 
good  lines,  yet  in  careless  hands  the  indurated  deposit  is  frequently  found  thick 
enough  to  interfere  with  the  adjustment.  And  this  must  be  attended  to  with  special  care 
when  colored  lines  are  to  be  drawn,  as  a  very  little  India  ink  will  ruin  the  brilliance  of 
any  other  color. 

The  adjusting  screws  of  the  pen  blades  are  apt  to  rust  if  care  be  not  taken  to 
prevent  it,  which  is  easily  done  by  the  occasional  application  of  a  drop  of  oil.  And 
indeed  the  like  attention  should  be  given  to  all  the  screws  of  all  the  instruments. 

51.  The  T-square  is  held   against   the   left-hand   end   or  the   lower  side  of  the  draw- 
ing board,  with  the  left  hand.      The   board   should   be   so   placed   as   to   receive   the   light 
from  the  upper   left-hand   corner;    and   horizontal   lines   are   drawn   by   the   upper  edge  of 
the   square,    never   by   the    lower   edge,    and    drawn    from    left    to    right,    the    pencil    being 
held   and   handled   precisely   like   the   pen,   as   described   in   the   preceding   section.       Ver- 
tical   lines   are    to    be   drawn    by   the   left-hand  edge   of   the    T-square    or    the   triangle,    as 
the  case  may  be,  the   hand  moving   always  away  from  the  body,  and   never  toward  it. 

Of  course  it  is  to  be  understood  that,  particularly  in  inking  in,  the  operator  is  at 
liberty  to  turn  the  board  around,  into  any  position  that  may  be  most  convenient :  the 
lines  in  that  case  will  be  drawn  by  that  edge  of  the  square  or  ruler  which  is  toward 
the  light. 

It  need  hardly  be  added,  that  the  pen  or  pencil  is  guided  by  the  upper  corner  of 
the  edge  of  the  ruier  in  use,  so  that  the  line  drawn  does  not  coincide  with  the  line 
of  contact  between  the  ruler  and  the  paper,  but  is  separated  from  it  by  a  distinct  line 
of  "  daylight."  Some  care  is  therefore  requisite  to  keep  the  marking  instrument  always 
vertical,  as  variations  in  its  position  will  make  the  line  wavy  instead  of  straight. 

52.  The  Triangles. — What   has   been   happily  called  "  a   fluent   use   of   the  triangles " 
is   as   important   to   the   draughtsman  as   ready   speech   to   an   orator;    and    there  are   bad 
as  well  as  good  ways  of  using  them. 

It  has  been  pointed  out  that  no  dependence  can  be  placed  upon  the  corners  of 
the  triangle,  which  are  sure  to  be  soon  rounded  off  by  use  if  not  so  to  begin  with. 
Yet  it  is  not  uncommon  to  see  the  attempt  made  to  draw  a  perpendicular  to  a  given 
line  at  a  given  point  upon  it,  by  placing  one  of  the  short  legs  in  exact  coincidence  with 
the  line,  the  right  angle  in  exact  coincidence  with  the  point,  and  then  marking  with  the 
pencil  along  the  other  leg ;  and  the  sight  would  be  exasperating  were  it  not  melancholy. 

If  one  triangle  be  held  stationary,  and  the  other  moved  along  so  that  its  hypothe- 
nuse  slides  on  one  of  the  sides  of  the  first,  a  series  of  parallels  can  be  drawn  by  one 
leg,  and  another  series,  at  right  angles  to  the  first,  by  the  other  leg.  And  by  grasping 
the  two  sides  which  are  in  contact,  it  is  as  easy  to  move  both  triangles  at  once  in 
adjusting  them,  as  either  one  alone ;  when  adjusted,  one  is  held  still  by  the  pressure  of 
the  left  hand :  the  thumb  and  little  finger  suffice,  leaving  the  other  fingers  free  to 
move  and  hold  the  other  triangle  as  desired. 

In  the  case  mentioned,  then,  a  correct  manipulation  would  be  to  set  one  leg  of  the 
moving  triangle  by  the  given  line,  and  then  sliding  it  along,  to  draw  the  required  line 
by  the  other  leg  through  the  given  point. 


92 


PRACTICAL  HINTS  FOR  DRAUGHTSMEN. 


Another  and  in  general  a  preferable  method  is  to  set  the  hypothenuse  of  the  mov- 
able triangle  by  the  given  line,  one  leg  being  in  contact  with  the  fixed  one:  the 
former  is  then  shifted  so  as  to  bring  the  other  leg  in  contact,  and  the  perpendicular 
drawn  by  the  hypothenuse,  which  will  now  be  at  right  angles  to  its  first  position. 

53.  It  is  to  be  particularly  observed,  that  in  "  setting "  a  triangle,  T-square,  or  any 
ruler  by  a  given  line,  no  attempt  is  made  to  bring  its  edge  into  actual  coincidence  with 
that  line ;  it  is  to  be  so  placed  that  the  given  line  could  be  redrawn,  or  produced  if 
required,  by  the  edge  in  question ;  which  will  therefore  be  separated  from  the  line 
itself  by  a  small,  uniformly  wide,  space  of  white  paper,  technically  called  "  day- 
light." So  also  in  setting  a  ruler  to  draw  a  line  through  two  given  points,  through 
a  given  point  in  a  given  direction,  through  a  given  point  and  tangent  to  a  given 
curve,  tangent  to  two  curves,  or  tangent  to  a  given  curve  and  in  a  given  direction :  in 
all  these  cases  the  accuracy  of  the  adjustment  depends  upon  the  certainty  with  which 
the  eye  can  judge  of  the  equality  of  the  minute  distances  measuring  the  "  daylight  " 
at  different  points,  and  this  certainty  is  practically  absolute. 

A  single  illustration  will  suffice  to  show  the  utility  of  a  pair  of  re- 
liable triangles.  Let  it  be  required  to  draw  a  right  line  tangent  to  two 
given  circles,  and  to  find  the  points  of  contact.  This  can  be  done  by  a 
geometrical  process,  but  much  more  readily  thus :  taking  the  two  triangles 
together,  set  the  hypothenuse  of  one  to  draw  the  tangent,  hold  the  other 
one  still,  turn  the  first  so  as  to  bring  the  other  leg  in  contact,  then  slide  it 
along  and  draw  lines  by  its  hypothenuse  through  the  two  centres  to  cut 
the  circumferences :  the  result  will  be  practically  more  to  be  depended 
on  than  that  of  a  geometrical  construction. 

54.  The  Curved  Rulers. — These   are   used,  as    has   been   explained,   for 
drawing   curves   through  points  determined  by  construction.     In  using  them, 
they  are  "  set "  so   that  some   part    of   the   ruler   in    hand   shall   enable    the 
operator    to   draw  a   portion    of    his    line ;    the    edge    not    passing   through, 
but  being  equidistant   from,  so  many  of   the  given   points   as   may  be. 

Now  in  order  to  make  sure  not  only  of  a  good  joining,  but  of 
proper  alignment  in  producing  the  curve,  this  precaution  must  be  care- 
fully observed ;  that  in  setting  the  new  sweep,  it  must  be  so  adjusted  as 
to  agree  with  a  part  of  the  line  already  drawn.  Otherwise,  the  eye  is  very 
likely  to  be  deceived,  and  the  new  part  of  the  line  is  apt  not  to  be  tan- 
gent to  the  first  part ;  the  result  being  painfully  evident  in  the  form  of 
a  "  hump  "  or  "  broken  back." 

55.  The  Pencil. — For   the  operations  of  mechanical   drawing,  the  pencil 
should    be  sharpened,    not    to  a  round   point,    but  to   an  edge;    not  a  square 
edge    like    that    of   a    chisel,    but    rather  like    a  duck's  bill ;    rounded   off   at 
the   end,  as  shown   in    Fig.  68  ;    and  the  flat   side  is   held   against  the  ruler, 
precisely  as  the  drawing  pen  is  held. 

By  trimming  the  pencil  in  this  way,  fine  clean  lines  can  be  drawn 
with  it  much  longer  than  if  it  were  cut  to  a  conical  point.  Some  make  use  of  fine 
sand  or  emery  paper  to  bring  the  pencil  to  an  edge ;  others  prefer  a  file ;  but  a  sharp 


FIG.  68. 


DRAWING   INSTRUMENTS  AND   MATERIALS.  93 

knife  is  better  than  either.  The  instrument  leads  are  trimmed  in  a  similar  manner, 
as  has  already  been  stated ;  and  so  set  in  the  clamp  as  to  have  the  edge  run  in 
the  direction  of  the  circumference  to  be  drawn. 

The  draughtsman  should  be  as  sparing  as  possible  in  the  use  of  the  pencil ;  the 
lines  should  be  fine,  because  the  ink  does  not  run  as  well  if  there  be  much  super- 
fluous pencil  lead  on  the  surface  of  the  paper ;  and  the  pencil  line  should  not  extend 
beyond  the  limit  of  the  proposed  ink  line  if  it  can  be  avoided. 

It  is  just  as  easy  to  leave  out  a  line  as  to  rub  it  out,  nay,  easier;  and  no  un- 
necessary ones  should  be  even  pencilled  in.  Lines  that  are  to  be  dotted  in  ink 
ought  always  to  be  dotted  in  pencil,  lest  the  fact  that  they  are  to  be  dotted  be 
forgotten  when  the  pen  is  taken  in  hand.  In  short,  the  pencil  drawing  should  look 
as  nearly  like  the  ink  drawing  as  possible  ;  the  advantage  is  readily  seen  when  it  is 
considered  that  if  time  presses,  tracings  must  often  be  made  from  the  pencil  drawing 
direct.  If  this  be  intended,  the  pencilling  should  be  heavier  than  if  the  sheet  is  to 
be  finished  in  ink. 

56.  The  Scale. — The  scale   should    never   be  used   as   a   ruler,  for  which   it  is  neither 
intended    nor  well    fitted.     It   should   be    used   only  for  setting   off   measurements   on  the 
drawing,  and   for   measuring   distances.     Its   utility   for   either   purpose   depends   upon   the 
perfection   of   its   edges,  and   the   accuracy   and   fineness   of  the   graduation;    and    nothing 
should  be  done  which  tends  to  injure  either. 

In  either  measuring  or  setting  off  distances,  the  scale  should  be  applied  directly  to 
the  drawing,  and  in  the  latter  operation,  the  points  should  be  marked  with  either  a 
needle,  or  a  finely  sharpened  pencil,  which  latter  is  in  general  the  better  instrument. 

The  compasses  and  dividers  should  be  applied  to  the  surface  of  the  scale  only  in 
urgent  cases:  in  setting  the  compasses  to  a  radius,  the  best  way  is  to  lay  the  scale 
on  the  paper  and  adjust  the  instrument  by  the  edge,  thus  avoiding  the  scratching  and 
defacing  of  the  graduations  by  the  needle-point. 

In  setting  off  a  number  of  consecutive  measurements  along  a  line,  as  A,  B, 
C,  D,  etc.,  it  is  perhaps  more  convenient  to  set  off  first  A,  then  to  move  the  scale 
and  lay  off  B,  then  from  the  third  point  to  set  off  C,  and  so  on,  since  in  each  case 
only  one  distance  requires  attention.  But  since  there  is  a  probable  error  in  each 
independent  operation,  and  at  least  an  even  chance  that  these  errors  will  accumulate 
instead  of  balancing,  this  is  not  an  advisable  method. 

The  proper  way  is  to  keep  the  scale  stationary ;  then  from  zero  set  off  in  succes- 
sion the  distances  A,A  +  B,  A  -j-  B -{-  C,  A  -\-B-\-  C-}-  D,  and  so  on  to  the  end,  or  as  far 
as  the  length  of  the  scale  will  permit.  In  this  way  it  is  ensured  that  the  whole  as  laid 
off  will  be  equal  to  the  sum  of  all  its  parts,  which  it  might  not  prove  to  be  if  the 
first  mode  of  operation  were  adopted. 

57.  General  Remarks. — It   is   hardly   necessary  to   suggest   to   any   one,  certainly  not 
to   him   who   has   made   his   outfit   pay   for   itself,  that   good   care   of   all   instruments   will 
be  found  profitable :  neglect  and  improper  usage  will  soon    ruin   a  set  which    if  treated  as 
it  should  be  would  do  good  service  for  two  generations  of  draughtsmen.     It  is  not  enough 
to   see   that   the   pens   are   always   clean   and    in   good   order ;    the    needle-points   and   the 
points  of  the  dividers   are  necessarily   extremely   sharp,  and    therefore    the   more    likely    to 


94  PRACTICAL   HINTS  FOR  DRAUGHTSMEN. 

be  broken  by  careless  handling.  If  this  happens,  no  attempt  should  be  made  to  use 
them  until  they  are  resharpened :  but  it  is  better  to  prevent  it.  When  not  in  use,  the 
instruments  should  be  replaced  in  the  case,  if  there  be  one ;  if  not,  a  piece  of  cork  is  a 
good  protection  to  the  points  of  dividers  and  the  blades  of  pens. 

In  order  to  do  good  work,  the  paper  must  be  kept  clean:  and  there  should  be  always 
at  hand  either  a  soft  feather  duster,  an  old  linen  handkerchief,  or  the  like,  with  which  to 
remove  not  only  dust,  but  more  particularly  the  detritus  left  after  using  the  rubber:  a 
particle  of  either  in  the  pen  is  sure  to  cause  annoyance,  if  not  to  spoil  the  lines. 

But  in  spite  of  all  care,  dust  or  dirt  will  eventually  adhere  to  the  wooden  instru- 
ments ;  if  this  be  allowed  to  go  on  to  any  great  extent,  it  will  be  impossible  to  keep 
the  paper  from  being  soiled  by  the  sliding  over  it  of  the  squares  and  triangles,  though 
they  be  ever  so  carefully  brushed.  It  is  well  to  know,  then,  that  this  closely  adhering 
dirt,  as  also  ink-stains  and  the  like,  may  be  removed  without  injuring  the  articles  in  the 
least  by  vigorous  rubbing  with  a  cloth  slightly  dampened  :  much  water  is  not  good,  but 
the  result  of  using  a  little  in  this  way  is  surprising  to  one  who  has  not  seen  it  tried. 


APPENDIX. 


THE  proportions  of  bolts,  nuts,  threads,  and  bolt-heads,  according  to  the  Sellers  system, 
adopted  as  the  U.  S.  standard,  are  given  in  the  first  of  the  annexed  tables. 

In  this  system  the  thread  of  the  screw  is  of  the  V  form,  with  its  surfaces  inclined  at  an 
angle  of  60°,  and  with  the  angles  cut  off  at  the  top  and  filled  in  at  the  bottom  to  the  extent 
of  one  eighth  of  the  depth  of  the  V-thread  each,  so  that  the  depth  of  the  thread  is  three 
fourths  that  of  the  full  V  form.  Or  it  may  be  defined  by  saying  that  the  breadth  of  the 
flat,  at  the  top  of  the  thread  and  also  at  the  bottom  of  the  groove,  is  one  eighth  of  the  pitch. 

Let  D  =  outside  diameter  of  belt, 

P  =  pitch  of  thread. 
Then  the  other  dimensions  given  in  the  tables  are  calculated  by  the  following  formulae,  viz. : 


P  =  0.24  VD  +  0.625  —  0.175  ; 

Number  of  threads  per  inch, 

Depth  of  thread,     . 

Diameter  inside  of  thread, 

Short  diameter  of  head  and  nut,  hexagonal  or  square,  . 

Depth  of  nut, 

Depth  of  head, 


^ 

P' 


2 

D; 

-D 

4 


The  number  of  threads  per  inch,  as  determined  by  these  formulae,  is  in  practice  so  far 
modified  as  to  use  the  nearest  convenient  aliquot  part  of  a  unit. 


U.  S.  STANDARD   SYSTEM. 


Diameter 
of 
Bolt. 

Threads 
per 
Inch. 

DIMENSIONS  OF  NUT. 

DIMENSIONS  OF  HEAD. 

Long  Diameter. 

Short 
Diameter. 

Depth. 

Long  Diameter. 

Short 
Diameter. 

Depth. 

Hexagonal. 

Square. 

Hexagonal. 

Square. 

i 

20 

A 

B 

1 

i 

9 
T» 

U 

i 

i 

A 

18 

H 

H 

if 

A 

H 

H 

if 

H 

1 

16 

If 

H 

U 

* 

I* 

H 

H 

U 

A 

M 

H 

'A 

H 

A            H 

'A 

H 

H 

i 

13 

i 

ii 

1 

i             i 

ii 

i 

A 

A 

12 

i* 

if 

H 

A 

ii 

i| 

H 

H 

* 

II 

iA 

ii 

»* 

t             'A 

ii 

'A 

H 

i 

10 

'* 

it 

i* 

i 

I* 

if 

i* 

1 

i 

9 

if* 

'A 

'A 

i 

<H 

2A 

tf 

H 

96 


APPENDIX. 


U.  S.  STANDARD   SYSTEM— Continued. 


Diameter 
of 
Bolt. 

Threads 
per 
Inch. 

DIMENSIONS  OF  NUT. 

DIMENSIONS  OF  HEAD. 

Long  Diameter. 

Short 
Diameter. 

Depth. 

Long  Diameter. 

Short 
Diameter. 

Depth. 

Hexagonal. 

Square. 

Hexagonal. 

Square. 

I 

8 

'i 

aft 

H 

I 

ii 

aft 

if 

if 

I* 

7 

2*                     2A 

I« 

I* 

*A 

«A 

iif 

ii 

Ii 

7 

aft               2H 

2                             Ii 

aft 

2|| 

2 

i 

If 

6 

2H 

3& 

2ft                        U                         *H 

3A 

*& 

•A 

Ii 

6 

2} 

3H 

2fl                          I*                         2} 

3« 

2| 

IT\ 

If 

Si 

2|i 

3f 

2ft                        I* 

»H 

34 

»ft 

iA 

I* 

5 

sft 

3i 

2*                          I* 

3ft 

3J 

2f 

if 

II 

5 

3H 

4A 

2  'ft                        I* 

3i! 

4ft 

HI 

I« 

2 

4i 

3tt 

4H 

3i                   2 

3H 

4il 

3i 

ift 

at 

4i 

4A                4H 

3i 

2i 

4SV 

4ii 

34 

if 

24 

4 

4lt                Stt 

3l 

24 

4JI 

stt 

3i 

iU 

2f 

4 

4ft               & 

4i 

2f                 4ll               6 

4i 

•i 

3 

34 

Stt               6tf 

4l 

3                    Sii               61* 

44 

•A 

3i 

34 

5H               7ft 

5 

3i                   Sli                7ft 

5 

24 

3* 

3i 

6A               7H 

51 

34                  6A 

7tt 

51 

2U 

3* 

3 

6*                  Si 

5* 

3*                   64 

8* 

5*                    2| 

4 

3 

7ft               8ft 

6i 

4                     7ft 

H* 

61 

aft 

4i 

•i 

74                9ft 

64 

4i 

7* 

9ft 

64 

3i 

4i 

2* 

7H 

9ll 

6| 

44 

7lf               9lt 

6| 

3ft 

4J 

2| 

81 

lot 

7i 

4i 

8f                ioj 

7i 

34 

5 

24 

8« 

IO|| 

74 

5 

8H 

toH 

74 

3U 

Si 

ai 

9i               "ft 

8 

5t 

9t                "ft 

8 

4 

54 

2f 

9H             «tt 

si 

5* 

9H          »H 

8f 

4ft 

5i 
6 

2| 
St 

IO&                  I2f 

iott          i2ff 

8} 

9i 

54                i  oft 
6                   ioi| 

I2f 
I2f! 

8| 

9l 

41 
4ft 

The  Whitworth  system,  which  is  extensively  used  in  England,  differs  from  the  Sellers 
system  chiefly  in  the  form  of  the  thread  ;  this  is  of  a  V  form,  with  the  surfaces  inclined  to 
each  other  at  an  angle  of  55°  instead  of  60°.  The  tops  of  the  threads  and  the  bottoms  of  the 
grooves  are  rounded  off  with  arcs  of  equal  radii,  of  such  magnitude  as  to  reduce  the  depth  of 
the  thread  to  two  thirds  that  of  the  original  V.  The  following  formulae  give  close  approxima- 
tions to  the  dimensions  in  the  second  table  : 


0.04; 
Number  of  threads  per  inch, 

Diameter  inside  of  thread,      ...... 

Short  diameter  of  head  and  nut,  hexagonal  or  square,  . 
Depth  of  nut,          ........ 


i 

P' 

o.gD  —  0.05  ; 
i.  5Z>  +  0.18; 
D. 


APPENDIX. 
WHITWORTH    SYSTEM. 


97 


Diameter 
of 
Bolt. 

Threads 
per 
Inch. 

Short 
Diameter. 
Head 
and  Nut. 

DEPTH. 

Diameter 
of 
Bolts. 

Threads 
per 
Inch. 

Short 
Diameter, 
Head 
and  Nut. 

DEPIH. 

Nut. 

Head. 

Nut. 

Head. 

i 

20 

I! 

i 

A 

If 

6 

2,', 

H 

lif 

& 

18 

i! 

A 

ii 

li 

6 

*H 

ii 

IT'* 

i 

16 

If 

i 

ii 

If 

5 

2fi 

'4 

IH 

A 

'4                     H 

A 

i 

Ii 

5 

2f 

if 

iH 

i 

«              !! 

i 

7 

TJ 

II 

4i 

3TV 

'I 

ifi 

* 

ii 

'A 

1 

IJ 

2 

4i 

3A 

2 

1} 

i 

IO 

'H 

* 

!i 

2i 

4 

3H 

2i 

ifi 

i 

9 

•H 

7 
S 

H 

2i 

4 

3li 

2i 

»A 

i 

8 

i« 

I 

1 

2f 

3* 

4A 

2f 

2H 

i* 

7 

i« 

I* 

H 

3 

3i 

4il 

3 

2| 

ii 

7 

z* 

Ii 

'A. 

The  third  table  gives  data  relating  to  standard  pipe-threads,  in  drawing  which  the 
following  instructions  are  to  be  observed : 

The  tube  is  tapered  on  the  outside  as  far  as  the  perfect  threads  extend;  back  of 
those  are  two  threads,  perfect  at  the  bottom  but  imperfect  at  the  top :  the  bottoms  of 
all  these  lie  in  a  line  parallel  to  the  outside  taper.  Beyond  these,  aga;n,  are  four  threads, 
imperfect  at  both  top  and  bottom :  the  manner  of  drawing  these  is  essentially  arbitrary. 

The  angle  of  the  thread  is  60°,  rounded  off  at  top  and  bottom  alike,  so  as  to  leave 
a  depth  of  |  the  pitch. 

STANDARD    DIMENSIONS   OF   WROUGHT-IRON   WELDED   TUBES. 


DIAMETER  OF  TUBE. 

THICKNESS  OF 
METAL. 

SCREWED  ENDS. 

Nominal 
Inside. 

Actual  Inside. 

Actual  Outside. 

Number  of 
Threads  per 
Inch. 

Length  of 
Perfect  Screw. 

Inches. 

Inches. 

Inches. 

Inch. 

No. 

Inch. 

l 

0.270 

0.405 

0.068 

27 

0.19 

i 

0.364 

0.540 

0.088 

18 

0.29 

= 

0.494 

0.675 

0.091 

18 

0.30 

i 

0.623 

0.840 

0.109 

14 

0-39 

i 

0.824 

1.050 

0.113 

14 

0.40 

i 

1.048 

1.315 

0.134 

ni 

0.51 

u 

1.380 

1.660 

0.140 

n| 

0-54 

'i 

1  .610 

1.900 

0.145 

Hi 

0-55 

2 

2.067 

2-375 

0.154 

ni 

0.58 

2i 

2.468 

2.875 

0.204 

8 

0.89 

3 

3.067 

3-500 

0.217 

8 

0.95 

3i 

3-548 

4.000 

0.226 

8 

1.  00 

4 

4.026 

4.500 

0.237 

8 

1.05 

4i 

4.508 

5-000 

0.246 

8 

I.IO 

5 

5-045 

5-563. 

0.259 

8 

1.16 

6 

6.065 

6.625 

0.280 

8 

1.26 

7 

7.023 

7.625 

0.301 

8 

1.36 

3 

7.982 

8.625 

0.322 

8 

1.46 

9 

9.OGO 

9.688 

0-344 

8 

i-57 

IO 

10.019 

10.750 

0.366 

8 

1.68 

Taper  of  conical  tube-ends,   I  in  32  to  axis  of  tube. 


INDEX. 


Air-pump — Sketch  of  Barrel 58 

Valve  for. 22 

Air-vessel 14 

B 

Bent  Lever 53 

Bevel  Wheels 27,  28 

Bolts — Conventional  Drawing  of  43 

Key 39 

Screw-driver  Heads 41 

Standing 39 

Tap 39 

Through .' 37 


Cam 5,55 

Centre-lines 50 

Check,  Vertical 32,  33 

Compass,  Beam 70 

Compasses 64 

Use  of 88 

Connecting-rod 31,  32 

Crank  and  Shaft 12 

Cross-head 55 

Curved  Rulers 78 

Forms 79 

Use  of 92 

Cylinder  and  Bracket 8 

"       and  Cover 4 

D 

Damp-stretching 86 

Dividers 63 

Use  of 89 

with  Tangent-screw 72 

DrawingBoard 73 

Paper 82 

Pen 67 

"    Use  of oo 

Pins 85 


Erasure  of  Pencil  Lines 83 

"       of  Ink          " 84 


Fillet  Lines 12 


H 


Hand-wheels. 


PAGE 

.   ii 


Imaginary  Lines 12 

Ink 84 

Chinese 85 

Colored  85 

Eraser 84 

Preparation  of 85 

J 

Jointed  Bows 70 


Large  Bolts — Method  of  Representing 4j 

Lengthening  Bar 66 

Link 19 

M 
i  Mounted  Paper 87 


N 

Needle-points 65 

Nut — Exact  Drawing  of 44 


Paper — Damp-stretching 86 

Drawing 82 

Mounted 87 

Tracing 88 

Pencil-holder 65 

Pencil — Method  of  Sharpening 92 

Pencils 83 

Use  of 93 

Pillow-block 14,  56 

Poppet-valve 23,  24 

Pulley  and  Shaft 10 

Pump-valve 21 

R 

Reversing  Link 61 

Riveted  Joint 6 

Rivets 45,  46 

Rock-shaft  and  Levers 19 

Rubber 83 


100 


INDEX. 


PAGE 

Scale 80 

Selection  of 82 

Triangular 82 

Use  of 93 

Screw — Wood 42 

Screws — Detail  Drawings  of 42 

Shaft  with  Crank 12 

with  Levers 19 

with  Loose  Collar 17 

Shifting  Points 65 

Size  of  Drawing  Board 7° 

Sketching  from  Measurement 48 

from  Memory 49 

without  Measurement 49 

Slide-valve 34,  35,  3& 

Spacing  Dividers 68 

Sponge — Rubber 84 

Spring  Bows ...    67 

Spur-wheels 24,  25,  26 

Stationary  Link 61 

Stuffing  Box  and  Gland 20 

Sweeps ~S 


Tests  of  Drawing  Board  and  T-square 76 

Thumb-tacks 85 


PAGE 

Tracing-cloth 87 

Triangles 77 

Test  of 77 

Use  of 91 

T   Square 74 

Shitting  Head 75 

Size  of 76 

Use  of 91 

U 
Unnecessary  Instruments  73 


Valve — Air-pump 21 

Chest 35 

Poppet 23,  24 

Slide 34,  3& 

Stem 52 

W 

Wheels— Bevel 28,  27 

Hand u 

Spur 24,  25,  26 

Worm 29,  30 

Wood-screw 42 

Writing  Paper  for  Diagrams 83 


OF  THB 

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